Muslims bring up this passage all the time, because James and the Jerusalem Church wanted Paul to be a good witness to the Jewish disciples and the unbelieving Jews, and the apostle Paul participating in Jewish temple sacrifices (the Nazarite vow – see Numbers 6:13-21) seems to contradict the teaching principle that Christ was the final sacrifice for sins – in Romans 6:10; I Peter 3:18; and Hebrews 7:27; 8:1-13; 9:12; 9:26; 10:10-14 (Christ was the final sacrifice, “once for all time”, “the new covenant”, etc.). The question is why would James and the Jerusalem insist upon this, seeing that Christ is the final sacrifice?
Granted, at first, in a surface reading, this seems like a difficult issue. This passage in Acts 21:17-26 is also the basis for some scholars believing that the Jewish disciples had a different belief / gospel than the so called “Pauline Christians” and they then make a big theory that the Jerusalem church, led by James and Peter, was not Trinitarian nor believed in Jesus as Son of God or “God in the flesh”; and that justification was not by faith alone, etc. (which would contradict Acts 15 and Galatians, which shows us that the Jewish disciples and Paul were completely in agreement on the gospel.)
If you keep reading all of Acts 21 to the end of chapter 28, you will see that this incident was what led to Paul’s arrest and being taken to Rome.
Acts 21:17-27 is historical narrative (what actually happened), and took place around 57 AD; after Paul wrote the book of Romans (during the time of Acts 20:2-3). It is not a teaching passage; so Romans 6:10; 1 Peter 3:18 and Hebrews 7:27; 8:1-13; 9:12; 9:26; 10:10-14 (once for all time) are the teaching principle, and the fact that Paul goes along with James in order to be sensitive to the Jews does not contradict, since Paul may have been wrong in doing that (we don’t know as the text does not say; only that it caused other Jews to attack him and lead to his arrest); – but God allowed him to do it in order to get him arrested, taken to Rome, and give 2 more opportunities for him to explain himself and his testimony, after Acts chapter 9, in Acts 22 and 26.
So, Paul was being sensitive to the Jewish disciples in Jerusalem and to James’ advice (see 1 Corinthians 9:19-23), but the unbelieving Jews from Asia (Acts 21:27) saw him there in the temple and assumed he was defiling the temple by bringing Gentiles into the temple.
This led to a mob scene and beating Paul and then the Romans arrested him (Acts 21:33) – the rest is about Paul’s defense (apologia / απολογια ) and opportunity to give his defense of his faith in Christ and as a Roman Citizen, to appeal to Caesar and go to Rome. It fits with the purpose of the whole book of Acts to show how the gospel spread from Jerusalem to the uttermost parts of the earth, Rome being the capital of the pagan Empire at the time and symbol of the gospel spreading into major Gentile lands. (see Acts 23:11)
It seems that the text in Acts 21 does not answer the question as to whether Paul (and James’ counsel and desire) was contradicting the book of Hebrews (written later in AD 68) or Romans 6:10 (written a little before the incident) or 1 Peter 3:18 (once for all time, used there also for Christ’s work on the cross, 1 Peter written around 64 AD.)
The apostle Paul may have thought in his mind, “I am doing this to be a good witness to the Jews (see 1 Corinthians 9:19-23); and I take these sacrifices as symbolic looking back to the sacrifice of Christ; and for the opportunity to be able to explain that these sacrifices are pointing to Christ as the final sacrifice”. The temple was still standing and operating, so it seems like a transitional period.
But neither James nor Paul require the Gentiles (Greeks, Romans, other cultures) to do the sacrifices. So it seems that Paul takes James advice to do the ritual, in order to show respect to the Jews. So Luke, the author of Luke-Acts is illustrating the principle of 1 Corinthians 9:19-23, and also showing how he is a student and fellow missionary on Paul’s missionary team. See the references to Luke in Colossians 4:14 and Philemon 24 and 2 Timothy 4:11; and the consistent teaching about the Lord’s supper in 1 Corinthians 11:20-34 with Luke 22:19-22; and Luke’s testimony of Jesus and the resurrection in Luke 24, and the necessity of the death, burial, and resurrection of Christ, and that the truths of Jesus suffering death, atonement, resurrection, and the preaching of that message to all nations were all written in the OT Scriptures. Also, the “we” passages of Acts 16 onward, show where Luke joined the team. All of these things together along with the testimony of the early church fathers demonstrate that Luke-Acts has apostolic authority and consistency with the apostle Paul’s teachings about Christ and salvation.
Just as I would never eat pork or drink wine in front of Muslims (even though I am free to do that – 1 Cor. 9:19-23), and I would take off my shoes when I visit a mosque – I am respecting their custom, even though that does not mean I agree with everything said inside the mosque.
I Cor. 9:19-23 is the principle; and Acts 21 demonstrates that Luke and Paul are consistent with one another.
But later, Jews who have come to believe Christ is the Messiah and the final sacrifice in Hebrews (68 AD), are told that they cannot reject that sacrifice as the final one, and go back to the temple and do sacrifices. Surely one of the purposes of writing the book of Hebrews around AD 68 was to show that Christ’s death was the final sacrifice once for all for sin (Hebrews 7:27; Hebrews chapter 8; Hebrews chapters 9 and 10, especially 9:12, 9:14, 9:22; 9:26, 9:28; 10:10-14, and 11:40 and 12:24, and 13:20-21) and that it was later after the incident in Acts 21 in 57 AD, is to show that they (Jerusalem church and James) should not do that anymore.
God then destroyed the temple in 70 AD to show that Christ was indeed the final sacrifice.
Addendum (November 28, 2016)
I am still wrestling with what Acts 21:17-26 exactly means, in light of 1 Corinthians 9:19-23 and the book of Galatians.
Here is an interesting point that I had not thought about, that the sacrifices at the end of the Nazarite vow were actually not performed yet. Maybe that is the key to the whole thing, God prevented Paul from violating the principles that will be laid out in the book of Hebrews, written a few years later.
“As James Boice argues (p. 364), the greatest proof that Paul was wrong was that God, who is sovereign over the details of our lives, intervened before Paul was able to offer the sacrifice in the temple and prevented him from doing it.”