I don't see how the new testament could be construed as anti-semetic. Jesus was focused on exposing the religious leadership of the Jews for their hypocrisy. His love for the people of Israel is apparent throughout the gospels.
Luke 19:41
And when he was come near, he beheld the city, and wept over it,
(Jerusalem)
Luke 13:34
O Jerusalem, Jerusalem, which killest the prophets, and stonest them that are sent unto thee; how often would I have gathered thy children together, as a hen doth gather her brood under her wings, and ye would not!
Matthew 10
5 These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not:
6 But go rather to the lost sheep of the house of Israel.
7 And as ye go, preach, saying, The kingdom of heaven is at hand.
Matthew 15:24
But he answered and said, I am not sent but unto the lost sheep of the house of Israel.
So if Jesus loves Israel, and the new testament is based on Jesus, how can the new testament be anti-semetic?
Jesus came and healed the lame, blind, lepors, demon possessed and those with many other afflictions (most of them Jews). It often says he did these things because he had compassion on them. How can this be anti-semetic?
Jesus only preached against the corrupt religous leadership of the time not against the nation of Israel.
Saved by an incredible Grace.