It's like social media. Europe was the Pope's subreddit. Don't piss off the moderator. It ain't rational but it's true.

It's even more like that than you might suspect; the old moderator stepped down (died) and the new one was a friend of Galileo, so he ignored warnings to not shitpost too much, and ate a very moderate "ban".

This can't be stressed enough.

He most certainly was not punished for any ideas, apart from making fun of the Pope and pissing off other people with power.