This narrative indicates that even Rabbis were in contact with Jewish Christians and that they exchanged interpretations and teachings.
It once happened that R. Eliezer was arrested on account of heresy and they brought him up to the bema to be tried. The hegemon asked him: Should an elder like you engage in those things? He answered: I consider the Judge trustworthy.
Now the hegemon thought that he had referred to him – though he referred only to his Father in Heaven – and so he said to him: Since you have deemed me reliable, I also said to myself, would these grey hairs err in those matters? (Surely not!) Dismissed! You are released (or “free of liability”). But when he left the court (= released from the bema), he was distressed to have been arrested on matters of heresy. His disciples came to console him, but he refused to accept [consolation].
R. Akiva came and said to him: Rabbi, may I say something to you, that you will not be distressed? He said: Speak. He said to him: Perhaps one of the heretics told you one of their heretical teachings which pleased you? He said to him: By Heaven! You reminded me!
Once I was strolling on the road (street) of Sepphoris when I met Yaakov from Kfar Sikhnin who told me a heretical teaching in the name of Jesus son of Pantiri and it pleased me. And I was arrested on account of heresy, for I transgressed the teachings of the Torah: “Keep your way far from her and do not go near the door of her house” (Prov 5:8). For R. Eliezer taught: One should always flee from what is ugly and from whatever appears to be ugly.