In fact the New Testament is anti-Gentiletic, not anti-Semitic as Jesus instructed(Matt 10:5) that his disciples should avoid Gentiles and Samaritans and go rather “to the lost sheep of the House of Israel.” Later,(Matt 15:24), he doubles-down and states that he came ONLY for “the lost sheep of the house of Israel.” Come on Gentiles. .. .where do we go to whine?!!
I think you miss the point - it’s perfectly fine with the Jews for the Apostles to go after the goyim. They don’t like ANYTHING that suggests he said to go after the choisen people.