My goodness. You gentlefolk are so persistent...in an odd thing. Do you want Christians to [be able to] lose their salvation?
There's absolutely no conflict between the John 10 and Hebrews 6 passages you quote. It's almost childish to circle and circle around this subject. If you yourself believe, and seek to love and know Him who saved/s you, and presumably your audience here does too, then who is this preaching directed to? The unbelievers or heretics? They've not even been saved the first time. The Christians here---to warn them? In case they get any ideas or temptations of falling away? What are we/they gonna do? Try harder? Save themselves harder? Watch-out harder? This paragraph alone confirms once born anew: always born anew. It's not something that can be undone. Even by God. Nor does He want to!
That paragraph alone put the lie to the Pelagianistic teaching that a believer can be re-damned. Salvation is a free gift by grace thru faith. Even the faith is the gift of God.
Jesus answered and said to her, If you knew the gift of God and who it is who says to you, Give Me a drink, you would have asked Him, and He would have given you living water. Jn 4:10.
For by grace you have been saved through faith, and this not of yourselves; it is the gift of God. Eph 2:8.
For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord. Rm 6:23.
But Peter said to him, May your silver go with you into destruction, because you thought that you would acquire the gift of God through money. Ac 8:20.
The word "gift" means that it's free. It's a gift. It's undeserved. It's not payment, it's not payment for faithfulness. It's not payment at all. The recipient, in this case, is utterly unworthy. Like myself. Not only unworthy, but impotent. Unable. Unable to save oneself. In fact, in point of fact: even dead. Eph 2:1, 5-6. That turns on the basic definition of "gift." In any language.
And the livingness, the life, the eternal life here received, Jn 3:16 and above, is not primarily talking about a pleasant nice eternity as opposed to eternal death and separation from God. Rather it's talking about regeneration. Being born anew. The life that is a unique and different life than the one we got from our parents. The life that is actually the life (I'd almost say "blood" by way of comparison)--the life of a new family. A real family: the family of God. That one can be born into. As wonderful as adoption is, it is categorically not adoption. But birth. Regeneration. (Hence the word "sonship" is a better translation than "adoption" in all cases in the New Testament.) In other words: it is the life of God. Eph 4:18.
So, in the first instance, God is the doer. He's the regenerator. One cannot "give back" one's life. (We cannot even destroy our lives--our souls will persist forever, since God created us.) One cannot return this gift. It's impossible because it's not merely a gift like a wrapped present, nor like a ticket to ride: it's a life. Not only is it a life, it's God's own life. What makes God God is His life. And not only is it His life: it's His birthing. His begetting.
Who were begotten not of blood, nor of the will of the flesh, nor of the will of man, but of God. Jn 1:13.
It's God who wants the family. It's His idea, His purpose. It's not our idea. He even goes so far as to predestine. To predestinate. Even the choice (His choice) is before the foundation of the world. That does not mean our choice is inoperative. It only means that His will is strongest. To see an unbeliever, like Saul of Tarsus, believe and receive, and then be baptized, is to confirm to him that "brother Saul, you were chosen before the foundation of the world. Now you're not only forgiven from your sins--you're born of God, through faith in His Son Christ Jesus." If Saul "falls away---big time"---or "small time," later, he doesn't need to redo all that he did. He can't! Not because he's really fallen "this time." But because he's already saved! Eternally. That's what Hebrews 6, indeed the entire book of Hebrews with its five warnings, is saying.
Here's a non-organic Pauline example: With the Olympic race, even today, in Barcelona or wherever: if the runner falls through tripping, he or she doesn't need to try to return to the starting line, "be saved" ("have been predestinated," have been chosen, repent, re-believe, be rebaptized, all over again). Such a thing is idiotic. It's not required. Because it's not necessary. It's not necessary because it's impossible. Once born of God, always born of God.
For it is impossible, in the case of those who have once been enlightened...to restore them again to repentance, since they are crucifying once again the Son of God to their own harm and holding him up to contempt (Heb 6) is not talking about being sorrowful or repentant for your sins or falling away. It's rather speaking of a sinner's first repentance. His or her initial repentance. What shames the Son of God is not that a believer fell, or that a believer apologizes----but that any believer would think (ready? Get this:)---that any believer would think that they "lost their salvation." And that they should or need to believe into Christ, receive Christ, profess faith in Christ, be saved from eternal damnation, all over again. That's the shame to Christ.
A (last?) point to be made about all this----no no, a second to last point---is that I'm reading in the Bible, and all of Christian history (and experiencing), that one cannot lose one's eternal salvation. One's eternal destiny, once one's been born from above, born of the Spirit. (That is an ontological change, a change in being.) I am not talking about gaining (or losing) salvation into the Millenial reign of Christ. I am not talking about not losing one's salvation into the Body and peace, practically and experientially, in this lifetime. I am not talking about being judged by God, whether now or in the next age (the Millenium). I am not talking about returning to one's own vomit or former lifestyle, or about temporarily being blotted out of the book of life, or being "dipped" into the lake of fire or second death. All those kinds of "perishings," "destructions," and "losing of salvations" are possible for believers. Of course. Including also passing through the last 3 1/2 years of this age, for immature or naughty believers alive then. Read Hebrews again. As severe as it, or any NT passage is, believers, the family and regenerated children of God, are in a completely different category from the unregenerate.
The "last" point is that believers can and do know and have the assurance that they're children of God. Not only objectively, factually Scripturally, but also subjectively and interiorly:
I have written these things to you that you may know that you have eternal life, to you who believe into the name of the Son of God...And we know that the Son of God has come and has given us an understanding that we might know Him who is true; and we are in Him who is true, in His Son Jesus Christ. This is the true God and eternal life. 1 Jn 5:13, 20.