Back On Hamster Wheel Of Sacrifice? S5e135 Acts21:24

4 guys are in the middle of a vow to the Lord that is lengthy, expensive, complicated, and confusing.  They are wrestling with the big question of "What will you do about your SIN?" Less so, what is our relationship with the charges of the Old Testament, especially if we are of the Jewish people? 
New school: It is all about Jesus. Once. For All. For all time. 
Old school: substitutionary animal sacrifice.  This was to point everybody to the fact that it was temporary, inadequate and frustrating.  Never enough. As soon as you are done you need to start over. Not sufficient.  All of it is just a reminder that WE NEED A SAVIOR.  

So why does Paul seem to compromise, or at least endorse their efforts? Some possibilities:
1. It is his plea that we should go back on the hamster wheel of animal sacrifice and wholly reject the finished work of the perfect sacrifice of Jesus.  If so, we should all be taking Nazarite vows every day for forever. NO. This isn't it. Galatians, 1 &2 Corinthians, and 1&2 Thessalonians and ROMANS has already been written, by Paul, clarifying his theology.
2. Paul is just in error.  He wouldn't be the first person, or congregation, or teacher, or disciple, or Apostle to be wrong just in the book of Acts. I don't think this is it either.
3. Paul is bending to the Jewish Christians a bit, to win them.  Or at least to keep winning them. Here is what he says in 1 Cor 9:20 To the Jews I became as a Jew, in order to win Jews. To those under the law I became as one under the law (though not being myself under the law) that I might win those under the law.  bewithme.us Google, Spotify, Deezer, apple podcasts.