Here is an interesting video from Iraq TV, courtesy of Memri:
I am not posting this to mock Muslims who maintain this belief, because they believe the Koran describes a flat earth. Rather, I post this because it is easier to make judgments about beliefs when others hold them. No Gadol nowadays maintains a belief in a flat earth, as far as I know. But to some rationalists, they and many non-rationalists maintain beliefs that could be comparable. Thus, some chareidim believe in a geocentric model of the universe, such that it was an ongoing dispute in certain chareidi papers in the lead-up to the recent Birkat Hachamma, and such that one chareidi Gadol said that to agree with Copernicus was heresy. More standard fare consists of disputes about the age of the universe, or over evolution.
Of course, distinctions can be made, and perhaps they should be made. But who did you side with in that video? What did you think of the epistemology, and the fellow's assumption that all modern science not in accordance with the Koran is false and heresy? This is appeal to authority, rather than facts, somewhat like (though not precisely like) asserting that the only valid and non-heretical way to understand a gemara nowadays is not like the Rishonim and in accordance what seems correct to one's intellect and true, but in accordance with the chareidi Gedolim and chareidi rabbinic leadership. What would you feel like if you were that Muslim rationalist in the video? How do you think a Jewish rationalist feels when presented with a similar appeal to authority?
Forget about the validity of the arguments. I am not trying to convince here, but rather trying to garner empathy and understanding for the rationalist position.