In the Middle East Islam became markedly more reactionary and narrowminded in the 18th century and AFAIK the reason exactly why this happened is not clear.
As I pointed out earlier, such tendencies generally happen in populations who feel they aren't getting their fair shake. The War of the Holy League at the end of the 17th century marks the start of a long period of decline for the Islamic world.
That's a factor, but too simplistic and too Eurocentric/Mediterranean. Decline of a Turkish great power doesn't explain religious changes among Arabs and Persians. Many living outside the Ottoman Empire.
Nobody here said Islam couldn't become more progressive. It's a very diverse religion with many traditions and there's always a potential for change. But, you have to take these religions as they are and as their practice and ideology exists today.
The point is those practices and "ideologies" are already much more diverse than we generally assume in the West.
You could add on to this the Jewish traditions of individual study and relative equality for women.
Is that why Jewish men thanked the Lord every day they were not born a woman?
I think traditional Judaism has about the same patriarchal gender roles as other traditional monotheistic religions, the equality is a bit of a myth with overemphasize on certain elements.
(but that is a bit of a detour from Islam..)
Its true that Judaism being a minority religion in Europe influenced it, but Euro-Islam is exactly that and being a minority in Europe and the US will influence Islam as well.
I would still say, that the real liberal versions of Judaism evolved in America AFAIK.