15 After these days we got ready and went up to Jerusalem. 16 And some of the disciples from Caesarea went with us, bringing us to the house of Mnason of Cyprus, an early disciple, with whom we should lodge.
17 When we had come to Jerusalem, the brothers received us gladly. 18 On the following day Paul went in with us to James, and all the elders were present. 19 After greeting them, he related one by one the things that God had done among the Gentiles through his ministry. 20 And when they heard it, they glorified God. And they said to him, “You see, brother, how many thousands there are among the Jews of those who have believed. They are all zealous for the law, 21 and they have been told about you that you teach all the Jews who are among the Gentiles to forsake Moses, telling them not to circumcise their children or walk according to our customs. 22 What then is to be done? They will certainly hear that you have come. 23 Do therefore what we tell you. We have four men who are under a vow; 24 take these men and purify yourself along with them and pay their expenses, so that they may shave their heads. Thus all will know that there is nothing in what they have been told about you, but that you yourself also live in observance of the law. 25 But as for the Gentiles who have believed, we have sent a letter with our judgment that they should abstain from what has been sacrificed to idols, and from blood, and from what has been strangled,  and from sexual immorality.” 26 Then Paul took the men, and the next day he purified himself along with them and went into the temple, giving notice when the days of purification would be fulfilled and the offering presented for each one of them.”(Acts 21:15-26 (ESV)
What better way to show that you do not forsake the law than to pay the expenses for four men to complete their vows? This was meant to show that Paul still had regard for the law of Moses. And we can see that he did in that he himself seems to have been under this same vow with these men. Paul could be a Jew to the Jews and a gentile to the gentiles in his work as an evangelist. He could even offer sacrifice in the temple. This of course was the expense that had to be paid for these men to be able to complete their vows, they had to by sacrificial victims. And Paul does! And this despite his faith in the once and for all perfect sacrifice of Jesus Christ on the Cross.
It was not as if worship in the Temple, and the temple sacrifices suddenly became sinful the day after Jesus rose from the dead. Jesus, of course, had made it unnecessary. Yet, for a time this would still be an act of devotion sanctioned by God. He still accepted the sacrifices of the pious there, still blessed them. The early church in Acts was said to have worshiped at the temple even daily. James himself would be murdered there, beaten with fullers clubs as he worshiped.
The destruction of the temple in 70 AD put an end to that. Even if a new temple was built and sacrifices began again, these would be sacrifices to a false god, to an idol, in as much as to worship there today would be an outright rejection of Jesus Christ as true God and true man as the once and for all final sacrifice for man, even as modern Judaism is the same. This however does not mean a person can’t respect and enjoy Jewish culture today the way Paul did then. It is ok to refrain from cheeseburgers, and eat pastrami on rye instead. Circumcision is nothing, as long as one is not imposing it upon you as a prerequisite for salvation.
It is a curious thing that the whole reason Paul makes this trip is to bring an donation to the church in Jerusalem, but once he gets there not a word of it is mentioned.