Galileo was facing some stiff odds when he published his Dialogue Concerning the Two Chief Systems of the World. He'd already been officially warned against heliocentrism, and he had enemies. But it's possible, just possible, that he would have squeaked by if he hadn't been a jerk to the Pope.
The feud between Galileo and the Catholic Church - the one that resulted in Galileo spending the last years of his life under house arrest - is perhaps the most well-known part of his history. Galileo was tried, threatened with torture, and forced to recant his perfectly correct position about the solar system being centered around the sun, instead of around the earth. What isn't as well known is the fact that Galileo was greatly supported by the Church up until he published this book, and was a particular friend of the reigning Pope at the time of his trial. What hung Galileo out to dry might very well not have been his intellectual position, but his attitude.
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