Question: After Yahushua's ultimate sacrifice, why did Paul circumcise Timothy in Acts 16 and also make a vow which included sacrifices in Acts 21:26?
Answer: Paul knew that there was no power or consequence in these Jewish practices, so he did such things just to avoid controversy with the Jews.
Peter said of Paul:
"As also in all his epistles, speaking in them of these things; in which are some things hard to be understood, which they that are unlearned and unstable wrest, as they do also the other scriptures, unto their own destruction." (2 Peter 3:16)
Paul said of himself:
"To the weak became I as weak, that I might gain the weak: I am made all things to all men, that I might by all means save some." (1 Cor. 9:22)
"Even as I please all men in all things, not seeking mine own profit, but the profit of many, that they may be saved." (1 Cor. 10:33)
He also admonished:
"If it be possible, as much as lieth in you, live peaceably with all men." (Romans 12:18)
"Follow peace with all men, and holiness, without which no man shall see Yahushua." (Hebrews 12:14)
See also his similar reasoning concerning meats offered to idols in 1 Cor. 8. (Read the whole chapter.)
"But meat commendeth us not to Yahuwah: for neither, if we eat, are we the better; neither, if we eat not, are we the worse." (1 Cor. 8:8)