John Gill Commentary Acts 18:15

"but if they are questions about words and names and your own law, look to it yourselves; I am not minded to be a judge of these matters." — Acts 18:15 (ASV)

But if it be a question of words
"Or of the word", what the Jews called the word of God, which Gallio did not pretend to understand: "and names"; as the names of God, of Jesus, and of Christ, whether he is God, and the Messiah:

and of your law ;
concerning circumcision, whether these Christians, and the proselytes they make, are obliged unto it:

look you to it ;
suggesting that this was a matter that lay before them, and they were the proper judges of, and might determine for themselves, since they had the free exercise of their religion, and a right of judging of everything that respected that within themselves, and for which they were best furnished, as having a more competent knowledge of them; as the Arabic version renders it, "and you are more learned in these things"; and most conversant with them:

for I will be no judge of such matters ;
and it would be well if every civil magistrate would act the same part, and not meddle with religious affairs, any further than to preserve the public peace.