Isn't teaching Torah just "Judaizing" or a different gospel?

No, and the verse usually thrown at this actually says the opposite. People quote Sha'ul (Paul) warning Titus about deceivers of the circumcision. But read three verses further and he names exactly who he means: men teaching Jewish myths and the commands of men, and doing it for dishonest gain (Titus 1:11, 1:14). In other words, the problem was man-made rules sold for profit, not God's actual instruction.

That is the very thing Yeshua confronted when He defended God's command against the tradition of men (Mark 7:9). He was not against the Torah. He was against the human additions piled on top of it.

So keeping what God actually said is not a different gospel, and it is not Judaizing. It is simply doing what the text says, which is what the earliest believers did.