Talmudic Judaism isn't exactly the religion of Jesus, since it wasn't invented yet

Well, Jesus obviously did not have Judaism as a religion - he was neither a Pharisee nor a Sadducee. But since Talmudic Judaism came after Jesus, it makes even less sense to argue that it would not be better for Jews to convert to Christianity... since they do not follow the religion they've had since immemorial, but the one that came after Christ.

I don't think that today's Jews get to wear Christianity's origin like armor. After schisms, people tend not to like each other very much.

Jesus and the Apostles were ethnic Jews. That is why it is stupid for any Christian to say that ethnic Jews are bad. They may freely argue that the religion isn't good though.