I believe that the Jews did refer to Gentiles as dogs, in a racist fashion.

The earliest Christians (known as the Nazarenes) were a sect/denomination of Judaism who believed Yeshua (Jesus) was the Messiah. They followed the Jewish laws and their leader James said that Gentiles could join but they had to at least follow the Noahide Laws (in Acts, the laws listed are the less offences, clearly there was never a question of Gentiles being able to murder/steal etc.). This was the case in most Jewish sects, Gentiles could be welcomed as Men of God without circumcision and full adherance to the law. It's still considered okay for gentiles within Judaism to stick to the Noahide laws.

If you read the Epistle to the Galatians (proven to be written by Paul) it's fairly clear that his enemies that he wants to castrate themselves are in fact the apostles of Jesus.