Trojan horse for rehabilitating religion.
Just because X is bad (I'm assuming you think religion is bad) and Y facilitates/rehabilitates/resembles X doesn't mean that Y must be wrong. Just because science historically hasn't been the perfect antithesis of science doesn't mean that science is religion, nor vice versa. It's just an inevitable consequence of the fact that people aren't perfect.
History and Philosophy of Science (HPS) is often criticized by hardcore atheists like Dawkins, because it draws attention to similarities and relationships between science and religion, throughout history and sometimes even in the modern age. Yeah, that can be a bit embarrassing to some. But it's not the historians' fault that a lot of European scientists in the early modern period casually crossed the boundary between science and religion every day. Whatever religious beliefs they had does not lessen the importance or correctness of their discoveries in any way.
If you don't like someone telling you a true story because your opponents would love to tell it, too, that's your problem. Lots of dictators also hate it when people tell true stories about them, but we tell them anyway because the stories are true.
It's not that I think they have any real chance of success with these tactics, but I do find this behaviour insulting. No good historian thinks such simplistic nonsense about the Galilean episode. Any good historian is well aware of the progressive simplification of the past. It's not that these specific points aren't all true, it's way they're used, the subtle insinuations, that I find slimy.
As for Feyeraband, well, again he's a favourite of the religious pundits - doesn't matter that none of his critiques of science really had an impact - again the suggestion is that hey, knowledge is limited, so all these scientists who like to think they're purveying ultimate truth are so silly, and maybe hey this religious stuff isn't all bad? Again it's insulting - any good scientist is highly aware of the limits of reliable knowledge - and anyway, just because there are some limits on the reliability of knowledge, doesn't mean we can't at least try and distinguish between more and less reliable knowledge. The religious pundits don't want us to do so, of course, they would rather that we get shocked over the hubris of prideful scientists, and walk around "knowing" that everything is relative, nothing is really knowable... Helps them out.
This is all textbook religious propaganda to me, the more so because it's so benignly packaged.
Historians of science need to stay away from both extremes: (a) the religious pundits who claim that science is just like religion, as well as (b) simplistic views of science that paint it as more objective and value-free than it really is. If every historian flocked to (b) just because they got annoyed of having their work co-opted by (a), we'd end up with an understanding of science that is just as unrealistic. Without a solid understanding of how social, psychological, and even religious factors influence science, how do we even go about trying to reduce such influences? You don't solve problems by pretending they don't exist. Who cares if Jerry Falwell's ilk use it in their propaganda, they bend and use everything in their propaganda anyway.
You inadvertently prove the point of the entire essay, which is that we all oversimplify and distort our stories of the past to serve our modern purposes. If you oppose religion because you think science and facts, however inconvenient, should be our guides, don't you have even more obligation than religious folks to avoid this kind of mistake?
Sure, the more random variations they came up with, the less credible the Ptolemaic model became. Occam's razor and whatnot. But the conclusive blow came much later than you might expect. Parallax was only verified in the 19th century, long after most scientists already gave up on geocentrism.