After hearing this, they praised God. And then they said, “You know, dear brother, how many thousands of Jews have also believed, and they all follow the law of Moses very seriously. But the Jewish believers here in Jerusalem have been told that you are teaching all the Jews who live among the Gentiles to turn their backs on the laws of Moses. They’ve heard that you teach them not to circumcise their children or follow other Jewish customs. What should we do? They will certainly hear that you have come. “Here’s what we want you to do. We have four men here who have completed their vow. Go with them to the Temple and join them in the purification ceremony, paying for them to have their heads ritually shaved. Then everyone will know that the rumors are all false and that you yourself observe the Jewish laws. “As for the Gentile believers, they should do what we already told them in a letter: They should abstain from eating food offered to idols, from consuming blood or the meat of strangled animals, and from sexual immorality.”
(‭Acts of the Apostles‬ ‭21‬:‭20-25‬ NLT)

This is a controversial passage. It is not to be understood as endorsing keeping the law of Moses. Paul was a Jew himself and had strong connection to the traditions of the Jews. He had observed the Law of Moses from a youth. He, in no way, was trying to disrespect the culture of the Jewish people. He was, however, preaching the freedom that comes through our Lord Jesus Christ. In fact, he had already written Romans, I and 2 Corinthians, and Galatians and each of them address this issue clearly. No matter what our traditions may teach us and no matter what culture we are from, we all must come through Jesus Christ for salvation. There is no other way.
We all have our own preferences and our own attachments to traditions that we may have observed through the years, perhaps even many years. However, we must never allow our traditions and cultural practices to replace the only atonement for our wicked sins - Jesus Christ. He, and He alone, can stand us right before God! (See Acts 4:12; I Timothy 2:5; John 14;6; Romans 5:1; 6:23; 7:1-6; Galatians 2:16; 3:23-28; Ephesians 2:8-10). It is abundantly clear in the scripture of the New Testament, that what Paul did here in Acts 21 was not to be made right with God, rather to be respectful to the Jewish customs. Being respectful to a custom doesn't mean we are compromising our faith, rather that we are trying to live out our faith in a way that we might possibly reach a culture for Christ. I Corinthians 9:19-23 says "Even though I am a free man with no master, I have become a slave to all people to bring many to Christ. When I was with the Jews, I lived like a Jew to bring the Jews to Christ. When I was with those who follow the Jewish law, I too lived under that law. Even though I am not subject to the law, I did this so I could bring to Christ those who are under the law. When I am with the Gentiles who do not follow the Jewish law, I too live apart from that law so I can bring them to Christ. But I do not ignore the law of God; I obey the law of Christ. When I am with those who are weak, I share their weakness, for I want to bring the weak to Christ. Yes, I try to find common ground with everyone, doing everything I can to save some. I do everything to spread the Good News and share in its blessings."(NLT). This doesn't mean that we do obvious, sinful things that we know are ungodly, but that we respect the customs and culture of people so long as it doesn't cause us to sin. In doing so, we reach into that culture with the good news of Jesus Christ, the Lord and Savior. The Jews were allowed to practice their customs as long as they knew that Jesus was the way of Salvation. In Acts 15 the Jerusalem Council discussed the issue and James, the Pastor, made the decision and made a declaration concerning this. The problem was that some of the Jews were still finding it hard to let go of their long standing customs as the way of acceptance to God.
In Numbers 6:1-21 we read about a purification vow. There were several requirements for the participant. It is possible that this is the vow Paul was asked to take and pay for. Certain things had to be purchased for its completion. Paul was not being hypocritical by participating, he was simply being personally respectful. There is nothing wrong with personal convictions and consecration so long as it isn't imposed upon everyone else as an act of redemption. Only Jesus can redeem us. Our lives, in regard to our personal convictions and consecrations, are our own choice. Customs, traditions, and other acts of personal preference can be helpful in our worship and honor of Jesus but must never be substituted as our earning salvation. We can't!! "Jesus paid it all! All to Him I owe! Sin had left a crimson stain. He washed it white as snow."