Leviticus 16 describes the rites of Yom Kippur (aka "The Day of Atonement"). In the first rite Aaron the high priest bathes in a Miktam making his body clean and dons linen underwear, a linen coat, linen sash and a linen turban. This was the garb of a regular priest, not the high priest. The high priest normally wore more decorative attire and an ephod "for glory and beauty" (Ex 28) but on this day of mourning for sin, he wore very simple, linen clothes. Isaiah prophesied a day when the people of God would no longer wear mourning clothes but would wear beauty, celebratory oils and garments of praise:
Isa 61:2 to proclaim the year of the LORD's favor, and the day of
vengeance of our God; to comfort all who mourn; Isa 61:3 to grant to
those who mourn in Zion— to give them a beautiful headdress instead of
ashes, the oil of gladness instead of mourning, the garment of praise
instead of a faint spirit; that they may be called oaks of
righteousness, the planting of the LORD, that he may be glorified.
Isa 61:10 I will greatly rejoice in the LORD; my soul shall exult in
my God, for he has clothed me with the garments of salvation; he has
covered me with the robe of righteousness, as a bridegroom decks
himself like a priest with a beautiful headdress, and as a bride
adorns herself with her jewels.
The next thing he would do is offer a male ox as a "burnt offering/"sin offering" for himself and his household. What I want to stress here is that at this point in the ritual the rites are for the preparation of the high priest so that he may enter the holiest place. It is in the holiest place that he will lay his hands on the head of the second goat, the living goat and figuratively place the sins of the People on it and then send it out alive outside of the camp:
Lev 16:6 "Aaron shall offer the bull as a sin offering for
himself and shall make atonement for himself and for his house.
... Lev 16:11 "Aaron shall present the bull as a sin offering for
himself, and shall make atonement for himself and for his house.
He shall kill the bull as a sin offering for himself. Lev 16:12
And he shall take a censer full of coals of fire from the altar before
the LORD, and two handfuls of sweet incense beaten small, and he shall
bring it inside the veil Lev 16:13 and put the incense on the fire
before the LORD, that the cloud of the incense may cover the mercy
seat that is over the testimony, so that he does not die. Lev
16:14 And he shall take some of the blood of the bull and sprinkle it
with his finger on the front of the mercy seat on the east side, and
in front of the mercy seat he shall sprinkle some of the blood with
his finger seven times.
There were 3 animals during this ceremony. The first was the bull that was offered for Aaron and his family, the last was the living goat that carried away the sins of the people and the second was another goat to make atonement for the people and to sanctify the altar:
Lev 16:15 "Then he shall kill the goat of the sin offering that is
for the people and bring its blood inside the veil and do with its
blood as he did with the blood of the bull, sprinkling it over the
mercy seat and in front of the mercy seat. Lev 16:16 Thus he shall
make atonement for the Holy Place, because of the uncleannesses of
the people of Israel and because of their transgressions, all their
sins. And so he shall do for the tent of meeting, which dwells with
them in the midst of their uncleannesses. Lev 16:17 No one may be
in the tent of meeting from the time he enters to make atonement in
the Holy Place until he comes out and has made atonement for himself
and for his house and for all the assembly of Israel. Lev 16:18 Then
he shall go out to the altar that is before the LORD and make
atonement for it, and shall take some of the blood of the bull and
some of the blood of the goat, and put it on the horns of the altar
all around. Lev 16:19 And he shall sprinkle some of the blood on it
with his finger seven times, and cleanse it and consecrate it from
the uncleannesses of the people of Israel.
So these first rites were all to express the remorse of the people and to prepare the chief priest and the altar so that the priest may conduct the real business of the day which was to lay his hands on the scape goat and let it go:
Lev 16:10 but the goat on which the lot fell for Azazel shall be
presented alive before the LORD to make atonement over it, that it may
be sent away into the wilderness to Azazel. ... Lev 16:20 "And when
he has made an end of atoning for the Holy Place and the tent of
meeting and the altar, he shall present the live goat. Lev 16:21 And
Aaron shall lay both his hands on the head of the live goat, and
confess over it all the iniquities of the people of Israel, and all
their transgressions, all their sins. And he shall put them on the
head of the goat and send it away into the wilderness by the hand of a
man who is in readiness. Lev 16:22 The goat shall bear all their
iniquities on itself to a remote area, and he shall let the goat go
free in the wilderness.
SO ALSO the death of Jesus was prepatory for priestly service and was not the actual intercession for the people!:
Heb 7:25 Consequently, he is able to save to the uttermost those who
draw near to God through him, since he always lives to make
intercession for them. Heb 7:26 For it was indeed fitting that we
should have such a high priest, holy, innocent, unstained, separated
from sinners, and exalted above the heavens. Heb 7:27 He has no
need, like those high priests, to offer sacrifices daily, first for
his own sins and then for those of the people, since he did this
once for all when he offered up himself. Heb 7:28 For the law
appoints men in their weakness as high priests, but the word of the
oath, which came later than the law, appoints a Son who has been
made perfect forever.
So my first point that I've tried to establish is that Hebrews 7:27 and 10:4 are NOT referring to the living goat of the ritual where the sins of the people were figuratively carried off but rather the preparatory rituals that allowed the priest to conduct that ritual without being killed for trespassing.
The theme of "To the Hebrews" is the idea that the Jewish believers no longer needed a temple, priests, offerings and what have you by showing that they are actually approaching the heavenly temple (the real temple), Jesus was a better high priest, offerings were no longer necessary, etc. So the argument we're in the midst of is the argument that Jesus is more qualified that the Aaronic priests to make intercession because:
- the Aaronic priests were mortal:
Heb 7:23 The former priests were many in number, because they were
prevented by death from continuing in office, Heb 7:24 but he holds
his priesthood permanently, because he continues forever. Heb 7:25
Consequently, he is able to save to the uttermost those who draw near
to God through him, since he always lives to make intercession for
them.
- their rituals did not perfect their natures so every year they had to repeat the ritual:
Heb 10:1 For the Law, being only a reflection of the blessings to
come and not their substance, can never make perfect those who come
near by the same sacrifices repeatedly offered year after year. Heb
10:2 Otherwise, would they not have stopped offering them, because
the worshipers, cleansed once for all, would no longer be aware of any
sins? Heb 10:3 Instead, through those sacrifices there is a reminder
of sins year after year, Heb 10:4 for it is impossible for the blood
of bulls and goats to take away sins.
By contrast, Jesus ever lives and HAS been made perfect:
Heb 10:11 Day after day every priest stands and repeatedly offers the
same sacrifices that can never take away sins. Heb 10:12 But when
this priest had offered for all time one sacrifice for sins, "he sat
down at the right hand of God."
Heb 7:26 For it was indeed fitting that we should have such a high
priest, holy, innocent, unstained, separated from sinners, and exalted
above the heavens. Heb 7:27 He has no need, like those high priests,
to offer sacrifices daily, first for his own sins and then for those
of the people, since he did this once for all when he offered up
himself. Heb 7:28 For the law appoints men in their weakness as
high priests, but the word of the oath, which came later than the law,
appoints a Son who has been made perfect forever.
He is forever free from sin and death:
Rom 6:9 Knowing that Christ being raised from the dead dieth no more;
death hath no more dominion over him. Rom 6:10 For in that he died,
he died unto sin once [a single time]: but in that he liveth, he liveth unto God.
Heb 9:22 And almost all things are by the law purged with blood; and
without shedding of blood is no remission. Heb 9:23 It was therefore
necessary that the patterns of things in the heavens should be
purified with these; but the heavenly things themselves with better
sacrifices than these. Heb 9:24 For Christ is not entered into the
holy places made with hands, which are the figures of the true; but
into heaven itself, now to appear in the presence of God for us: Heb
9:25 Nor yet that he should offer himself often, as the high priest
entereth into the holy place every year with blood of others; Heb
9:26 For then must he often have suffered since the foundation of the
world: but now once in the end of the world hath he appeared to put
away sin by the sacrifice of himself. Heb 9:27 And as it is
appointed unto men once to die, but after this the judgment: Heb 9:28
So Christ was once offered to bear the sins of many; and unto them
that look for him shall he appear the second time without sin unto
salvation.
BUT the apparent contradiction of the OP is actually a confusion of referents. The passage in Leviticus is referring to the overall result of the Yom Kippur ritual, that the sins of the people were actually followed with the forgiveness of the sins of the people while the Hebrews 10 assertion is that the preparatory ritual where the priest atones for himself and his family was limited in that his sins were forgiven but he himself was not made perfect.
It is important to understand that the ritual of Yom Kippur was NOT just theater but was actually the way that God DID forgive the sins of the people, as stated in Leviticus 16:30, as noted in the OP:
Lev_4:20 And he shall do with the bullock as he did with the bullock
for a sin offering, so shall he do with this: and the priest shall
make an atonement for them, and it shall be forgiven them. Lev_4:26
And he shall burn all his fat upon the altar, as the fat of the
sacrifice of peace offerings: and the priest shall make an atonement
for him as concerning his sin, and it shall be forgiven him. Lev_4:31
And he shall take away all the fat thereof, as the fat is taken away
from off the sacrifice of peace offerings; and the priest shall burn
it upon the altar for a sweet savour unto the LORD; and the priest
shall make an atonement for him, and it shall be forgiven him.
Lev_4:35 And he shall take away all the fat thereof, as the fat of
the lamb is taken away from the sacrifice of the peace offerings; and
the priest shall burn them upon the altar, according to the offerings
made by fire unto the LORD: and the priest shall make an atonement for
his sin that he hath committed, and it shall be forgiven him.
Lev_5:10 And he shall offer the second for a burnt offering,
according to the manner: and the priest shall make an atonement for
him for his sin which he hath sinned, and it shall be forgiven him.
Lev_5:13 And the priest shall make an atonement for him as touching
his sin that he hath sinned in one of these, and it shall be forgiven
him: and the remnant shall be the priest's, as a meat offering.
Lev_5:16 And he shall make amends for the harm that he hath done in
the holy thing, and shall add the fifth part thereto, and give it unto
the priest: and the priest shall make an atonement for him with the
ram of the trespass offering, and it shall be forgiven him. Lev_5:18
And he shall bring a ram without blemish out of the flock, with thy
estimation, for a trespass offering, unto the priest: and the priest
shall make an atonement for him concerning his ignorance wherein he
erred and wist it not, and it shall be forgiven him. Lev_6:7 And the
priest shall make an atonement for him before the LORD: and it shall
be forgiven him for any thing of all that he hath done in trespassing
therein. Lev_19:22 And the priest shall make an atonement for him
with the ram of the trespass offering before the LORD for his sin
which he hath done: and the sin which he hath done shall be forgiven
him. Num_14:19 Pardon, I beseech thee, the iniquity of this people
according unto the greatness of thy mercy, and as thou hast forgiven
this people, from Egypt even until now. Num_15:25 And the priest
shall make an atonement for all the congregation of the children of
Israel, and it shall be forgiven them; for it is ignorance: and they
shall bring their offering, a sacrifice made by fire unto the LORD,
and their sin offering before the LORD, for their ignorance:
Num_15:26 And it shall be forgiven all the congregation of the
children of Israel, and the stranger that sojourneth among them;
seeing all the people were in ignorance.
Rom 3:25 Whom God hath set forth to be a propitiation through faith
in his blood, to declare his righteousness for the remission of sins
that are past, through the forbearance of God;
However, it made nothing perfect. Everyone left the ritual and went back to sinning.
AND, YHVH complains that the People have all, to a man, forsaken his ways and abandoned his laws:
Heb 8:7 For if that first covenant had been faultless, then should no
place have been sought for the second. Heb 8:8 For finding fault
with them, he saith, Behold, the days come, saith the Lord, when I
will make a new covenant with the house of Israel and with the house
of Judah: Heb 8:9 Not according to the covenant that I made with
their fathers in the day when I took them by the hand to lead them out
of the land of Egypt; because they continued not in my covenant, and I
regarded them not, saith the Lord.
So the Jews did find forgiveness of their sins on Yom Kippur but they did not continue in the covenant. They would sin willfully and grievously so another covenant had to be forged.
So to the original questions:
- Is Hebrews talking about future sins?
Yes.
- Is Hebrews saying that it was possible, but something changed and it's now impossible?
Yes.
- Can one be "clean from sin" without sins being "taken away"?
Yes, sins can be forgiven without sins being taken away but they will "re-present".