It kinda feels like you’re pushing an anti-Semitic narrative here instead of trying to argue the history.

The Jewish people were not some minor cult. The story does go that the Jewish authorities did argue for Jesus to be executed, part of it definitely being because of his “king of the Jews” thing. Judaism as a religion and The Jewish people are not 1 and the same in context, Jesus famously was not anti-Roman and argued his teachings were of the mind.

The Romans were famous for incorporating local government structures and religions as long as you paid and served.

Yes according to the myth the Jewish Authorities ( again, integrated and part of the Roman governing of the area) pushed for him to be executed for claiming to be the king of the Jews (political) which would upset Roman rule.

Again, this is of course assuming you believe the myth that actually isn’t written about or recorded at all until a couple generations later.

There aren’t Roman records of the event until later, after the fact. From people who weren’t there, but heard about it from people who were or heard it from folks who were … etc.

Not an answer

There is no contemporary record of Jesus or his crucifixion.