Paul didn't try to avoid the trap, he was given permission to explain who he was before his conversion and that silenced the Jews. It turned out to be a great Gospel opportunity for him.Acts 21 is Paul knowingly and willingly walking into a trap laid for him by the Jews.
the vow is the binding of his hands and feet at the hands of the Jews with "his own belt" as prophesied ((vv. 10-11))
the Jews did not physically tie him up; the Romans did. the Jews deceitfully bound him with a voluntary vow ((this was not the keeping of the Law)), then knowing where he was, having him surrounded and captive at the temple, seized him & handed him over to the Gentiles.
It sounds like most of the Jews who converted, still kept the law. Just as many Gentile Christians choose to keep some of the old covenant laws to this day, so it's a case of allowing believers to observe as much or as little of the non essential old covenant laws.
Some Christians drink alcohol and others don't, some eat pork and others don't so it's an individual preference thing which shouldn't be a stumbling block for fellowship.