The "conflict thesis" version of the Galileo affair (lone scientist sticking up against the dogma of religion, never bowing, persecuted just for seeking the truth, etc.) is a 19th-century creation. The people who championed it were people who were trying to organize a new "scientific" understanding and an accompanying identity that went with it, which they saw largely as being about the rejection of religion as a form of authority about the natural world. This was during a period when science was beginning to "professionalize" (the term "scientist" had only been coined in 1834), and the context included discussions about Darwinism, evolution, etc.

A lot of "bad history of science about religion" dates from this period. The two biggest "contributors" to this are John William Draper and Andrew Dickson White, who more or less cooked up the idea that science has always been at conflict with religion (the aforementioned "conflict thesis") and provided very poor, narrow readings of history as evidence for this. For many decades now, historians have known that this history is very inaccurate, that the relationship between science and religion is far more complex (at times, religion was the main sponsor and motivation for scientific work, for example) and varies by time/place/etc. Most historians of science today see the Galileo affair as being as much about relatively local Papal politics, and some poor decisions on Galileo's part, and it is overall just a more complicated story (that doesn't mean that Galileo didn't get a raw deal, to be sure, but it complicates a simple "religion vs. science" or even "Catholic Church vs. science" reading considerably). But the simple myth appeals strongly to scientists and people who think that the acceptance of science means the rejection of other forms of authority (religion, politics, etc.), and so it propagates nevertheless. There are many other such myths.