The fact that when this topic comes up, a reference to Galileo is always made shows us just how infrequent the Church's outright persecution of science and natural philosophy was.
Christianity was the main patron of science, natural philosophy, and universities in Europe for one thousand years.
There is no denying that there was periodic conflict between scholarship and the church occurred. But the Galileo affair is far more nuanced than most people realize.
Galileo's theory was rejected because it was a hypothesis without any substantial proof. The Vatican was willing to consider alternatives to the Aristotelian geocentric universe. But they were not going to accept any old hypothesis which came along.
Galileo had a hypothesis, but he did not have a mechanism, the mathematics, or satisfactory physical explanation. The Vatican had their own scientists - the Jesuits - look at Galileo's hypothesis and found it was not substantiated by physics as it was understood at the time. First, this was before we understood the laws of inertia. So it did not make sense based on the physics of the day that the earth could be spinning at thousands of miles per hour, without throwing people off balance, or even into outer space.
We had to wait for Newton's first law of mechanics to see in hindsight that what Galileo hypothesized could make sense.
Second, based on the state of scientific knowlege at the time, we did not know the stars were vast light years in distance from us. The expectation at the time is that if Galileo's hypothesis were correct, they would observe stellar parallax.
They did not observe stellar parallax.
We had to wait 100 years for Newton's first law, and his law of gravitation to have the mathematics and physics to substantiate Galileo's hypothesis.
As for Galileo's persecution after his second trial, that was more political than religious in nature. Galileo had an offensive personality, he offended many powerful people, and his persecution was caught up in the politics of the counter reformation.
Sidebar: Monks and Priests of the 19th and 20th centuries made important, even seminal scientific contributions.
I agree with you that the modem GOP and their fundamentalist base are hostile to science