And here's what Peter had to say about it:
Acts 15:9 (KJV) And put no difference between us and them, purifying their hearts by faith.
Acts 15:11 (KJV) But we believe that through the grace of the Lord Jesus Christ we shall be saved, even as they.
So where's the difference?
Yep, the council of Jerusalem should put it to rest that they were all on board with the same gospel of salvation unto eternal life which was only by the death and resurrection of the Lord Jesus Christ.
And yeah, those two verses you listed are clear as a bell.
They all believed God put no difference between the believers Peter and Paul were preaching to, and that they would all be saved the same way.
The "purifying their hearts by faith" in verse 9 is the circumcision of the heart.
And the Amos 9 quote James uses seals the deal as it is prophetic of them all being of the same tabernacle/temple/body of Christ.
Acts 15:16-17 KJV
(16) After this I will return, and will build again the tabernacle of David, which is fallen down; and I will build again the ruins thereof, and I will set it up:
(17) That the residue of men [mankind] might seek after the Lord, and all the Gentiles, upon whom my name is called, saith the Lord, who doeth all these things.
James doesn't equate the restored tabernacle of David as any literal dwelling structure or literal ethnic group, but equates it theoretically to the body of a single individual --- the resurrected Lord and Savior Jesus Christ.
Just as Paul refers to a "tabernacle" as a body ---- 2 Cor 5:1 & 4.
So does Peter ---- 2 Peter 1:14.
And the author of Hebrews --- Heb 9:11.
The restored tabernacle is the body of Jesus restored from death at the resurrection.
It (His body/tabernacle) is the dwelling of all believers of the whole world of all nations.
And all of them, including Paul, are in agreement.
That prophesies were taken theoretically instead of literally happens often by the NT believers led by the Spirit.
Matthew does it with "out of Egypt I called my son".
By a literal reading of the prophesy he is quoting one sees it is speaking of the descendants of Jacob, but Matthew equates it theoretically as a single individual --- the Lord Jesus Christ.
Mat 2:15
Hos 11:1
Paul does the same here with the "seed".
By a literal reading of the prophetic saying one sees it is speaking of the descendants of Jacob, but Paul is equating it theologically to a single individual --- the Lord Jesus Christ.
Gal 3:16
Does that mean there will never be a literal restoration of the kingdom of Israel in the promised land as spoken by Amos and other prophets?
No.
But it does tell us that there is a much higher and deeper significance to all of it.