The Jerusalem Council addressed only one specific ordinance: circumcision. It neither had authority, nor interest, in changing the dietary health laws.
And certain men which came down from Judaea taught the brethren, and
said, Except ye be circumcised after the manner of Moses, ye cannot be
saved. (Acts 15:1, KJV)
When therefore Paul and Barnabas had no small dissension and
disputation with them, they determined that Paul and Barnabas, and
certain other of them, should go up to Jerusalem unto the apostles and
elders about this question. (Acts 15:2, KJV)
Circumcision was supposed to be done on the eighth day after birth. While there are examples of full-grown men being circumcised, as also was Abraham, to whom the rite was first given, it is a very uncomfortable and disagreeable procedure at such a stage of one's life.
For the Gentiles, God had already shown by pouring out His spirit on them, that He accepted them while yet uncircumcised. The Jerusalem Council, therefore, concluded that this signal from God meant that the church no longer needed to enforce this ritual upon the Gentiles when they became Christians.
The Council itself maintained the dietary ordinances and other ordinances, appearing to make exception only on the question of circumcision.
For it seemed good to the Holy Ghost, and to us, to lay upon you no
greater burden than these necessary things; (Acts 15:28, KJV)
That ye abstain from meats offered to idols, and from blood, and from
things strangled, and from fornication: from which if ye keep
yourselves, ye shall do well. Fare ye well. (Acts 15:29, KJV)
These rules were standard, and unchanged. Leviticus 3:17, for example, makes clear that blood should not be eaten--which is why a strangled animal was unfit for consumption, because the blood was not drained properly from it.
It shall be a perpetual statute for your generations throughout all
your dwellings, that ye eat neither fat nor blood. (Leviticus 3:17,
Blood was always unclean. Fat was always unclean. The Jerusalem Council did not change these things. They actually added to the restrictions in saying that people should not eat foods that had been offered to idols.
In fact, the Greek word εἰδωλόθυτος (eidolothytos) translated in the KJV as "meats offered unto idols," does not refer to "meat" (as in flesh food) at all. It just means anything that might have been offered to idols. The ESV has it as "what has been sacrificed to idols."
Clearly, the Jerusalem Council was not negating any of the Levitical laws, with one exception, this one:
And in the eighth day the flesh of his foreskin shall be circumcised.
(Leviticus 12:3, KJV)
Circumcision a Sign of the Covenant
Unlike the health laws, such as those of clean and unclean meats, circumcision had but one purpose: it was a sign of entering into a covenant relationship with God.
This covenant is sometimes called the "Abrahamic covenant" because this symbol had first been given to Abraham.
This is my covenant, which ye shall keep, between me and you and thy
seed after thee; Every man child among you shall be circumcised. And
ye shall circumcise the flesh of your foreskin; and it shall be a
token of the covenant betwixt me and you. (Genesis 17:10-11, KJV)
Circumcision was only a "token." It was not the covenant itself. There was no special power in it, just as there is no special power in a wedding ring, which is also a token, to keep the marriage together.
God Suspended the Token during the 40 Years in the Wilderness
Because the Israelites had rebelled at Kadeshbarnea, listening to the evil report of the 10 spies, then, regretting their choice after God sentenced them to 40 years in the wilderness and choosing to go fight without God's permission, God had suspended the token of His covenant with them.
||Book of Joshua -- At the entrance to Canaan
||At that time the LORD said unto Joshua, Make thee sharp knives, and circumcise again the children of Israel the second time.
||And Joshua made him sharp knives, and circumcised the children of Israel at the hill of the foreskins.
||And this is the cause why Joshua did circumcise: All the people that came out of Egypt, that were males, even all the men of war, died in the wilderness by the way, after they came out of Egypt.
||Now all the people that came out were circumcised: but all the people that were born in the wilderness by the way as they came forth out of Egypt, them they had not circumcised.
||For the children of Israel walked forty years in the wilderness, till all the people that were men of war, which came out of Egypt, were consumed, because they obeyed not the voice of the LORD: unto whom the LORD sware that he would not show them the land, which the LORD sware unto their fathers that he would give us, a land that floweth with milk and honey.
||And their children, whom he raised up in their stead, them Joshua circumcised: for they were uncircumcised, because they had not circumcised them by the way.
Rebellious people could not honestly bear the token of God's covenant; and God suspended it. At the Jerusalem Council, then, as the apostles had witnessed that God's spirit had already given token of His acceptance of the Gentile believers, they realized that, once again, the physical token had been superseded and was no longer truly necessary.
No, the Jerusalem Council did not allow believers to eat rabbit meat, nor any other unclean meats. The Council addressed specifically the requirement of circumcision for the Gentile believers whom God had already shown His acceptance by pouring His spirit upon them, and, based on this evidence, abolished this requirement.