Jesus did seem to win many gentiles but He held off on actually converting them to Judaism. Instead, He wanted them to wait until after the passion. There is a good reason He did this.
When Jesus went to Syria many crowds followed Him and He healed them all. But now we see people hating on the Syrian people and it's a shame because Jesus loved them a lot.
And his fame went throughout all Syria: and they brought unto him all sick people that were taken with divers diseases and torments, and those which were possessed with devils, and those which were lunatick, and those that had the palsy; and he healed them. (Matthew 4:24)
When Jesus went to the country of the Gergesenes; He delivered a man with many demons who was quite possibly a gentile. The country of the Gergesenes was actually an area that had been colonised by Greeks. They built 10 cities there and so the name of that region was "decapolis" or translated from Greek; it is 10 cities.
And when he was come to the other side into the country of the Gergesenes, there met him two possessed with devils, coming out of the tombs, exceeding fierce, so that no man might pass by that way. (Matthew 8:28)
Note, that Jesus did not let this man follow Him after He was delivered from the demons. Instead, Jesus told him to go home to his home city and tell everyone about what God had done for him. So, Jesus apparently did not demand that he convert to Judaism.
Jesus also went to the Samaritans and many of them believed in Him.
And said unto the woman, Now we believe, not because of thy saying: for we have heard him ourselves, and know that this is indeed the Christ, the Saviour of the world. (John 4:42)
Later, some Greeks heard about Jesus and wanted to see Him, but it is not recorded that Jesus spoke to them. Only He said that "a corn of wheat" abides alone unless it falls in the ground and dies. By this Jesus was signifying that the gentiles would be saved through His death.
And there were certain Greeks among them that came up to worship at the feast:
The same came therefore to Philip, which was of Bethsaida of Galilee, and desired him, saying, Sir, we would see Jesus.
Philip cometh and telleth Andrew: and again Andrew and Philip tell Jesus.
And Jesus answered them, saying, The hour is come, that the Son of man should be glorified.
Verily, verily, I say unto you, Except a corn of wheat fall into the ground and die, it abideth alone: but if it die, it bringeth forth much fruit. (Excerpt John 12)
In conclusion Jesus message to the gentiles He met everywhere was not to convert to Judaism. Rather it was for them to wait until after the "passion" was fulfilled. That is the death, burial and resurrection. Then they would be saved by the gospel.
As it was promised of the Messiah:
And he said, It is a light thing that thou shouldest be my servant to raise up the tribes of Jacob, and to restore the preserved of Israel: I will also give thee for a light to the Gentiles, that thou mayest be my salvation unto the end of the earth. (Isaiah 49:6)
