They are, but in the same time they are not. Incompatibilities arise when people based on religion try to debunk some proven scientific facts. Darwin's evolution theory being one of the most famous examples of that. Flat earthers also based their proves on the Bible. But in the same time, some important scientific development did benefit from religion. For a long time, most scientists could be found in the monastery. Medical science in particular was known to be practiced by monks and nuns. In the Dutch language (I do not know about English or other languages), nurses are often called "zuster" which literally means "sister". The pronoun to refer a nun by is also "sister". Yes, that ain't a coincidence, that came from the time that nurses were most of all nuns.
Perhaps the reason that in RPG games the healers are quite often clerics is based on this fact too.
Of course, we should also note the philosophies behind religions differ per religion, and most religion have multiple versions and then the philosophies could also differ on vital points. Some religions are stricter in denying scientific facts than others, and some even embrace a lot of scientific facts as basis on their philosophies. The founder of the Scientology religion was even an author of science fiction stories. Now I'm not saying I know Scientology very well or its full background, but you if its founder was against science in general, he'd likely also not be in science fiction... But I could be wrong on that one.
Most of the "incompatibilities" began when scientists found prove of some stories stated by the church were in fact wrong. These stories could damage the power of the church. The question is, is religion or lust for power the reason of the "incompatibility". We all know the church doesn't have a clean history in this department.
So science and religion being incompatible is not exactly a lie, but not exactly the truth either.