It was a little more complicated as to whether the priests (and other astronomers) knew he was right.
Heliocentrism made a specific prediction of parallax --- namely that the stars would move back and forth over the course of a year. But this wasn't observed which is one of the main reasons that many astronomers remained skeptical of the idea. Tycho Brahe proposed an alternative model that adopted many of the advantages of heliocentrism but didn't have the parallax problem. In his theory all the planets revolved around the Sun, but the Sun revolved around the Earth.
Of course it turned out that the stars were much, much further away than anyone expected, so the parallax effect was too small to be seen until the 19th century.
But your broader point is correct, Galileo's troubles were brought about more due to his political indiscretions than his astronomy per se.
Heliocentrism made a specific prediction of parallax --- namely that the stars would move back and forth over the course of a year. But this wasn't observed which is one of the main reasons that many astronomers remained skeptical of the idea. Tycho Brahe proposed an alternative model that adopted many of the advantages of heliocentrism but didn't have the parallax problem. In his theory all the planets revolved around the Sun, but the Sun revolved around the Earth.
Of course it turned out that the stars were much, much further away than anyone expected, so the parallax effect was too small to be seen until the 19th century.
But your broader point is correct, Galileo's troubles were brought about more due to his political indiscretions than his astronomy per se.