Saying 'extreme Islam' is a backlash against Western feminism ignores a few things.
All conservative factions of religions have had an uprise globally over the last couple of decades. All of them, not just Islam. There are many reasons for this - they tend to be the groups openly trying to convert others, openly attach their charity to their faith, give very absolute answers which some find comforting, and so on. Hasidic Judaism is on the rise and has given birth to the Hasidic Noachide movement over the last few decades having an even wider reach. There are so many other dynamics at play.
The most Islamic countries repeatedly given as examples in this thread were liberal in the 70s and it wasn't feminism that caused either revolution (Iran's was backed by Britain, Afghanistan's was backed by US, Israel's more religious conservatism has foreign backing). Ignoring that these revolutions were heavily pushed by imperialistic efforts by Western countries to become more conservative ignores that Western governments and corporation see a benefit to this and have backed this to the point of a supporting and pushing these forward. We must question what the West is gaining if we hope to actually challenge something that the West supported in the first place.
That there are feminist movements within Islam, as well as around the world in post colonial feminism, and Western feminism isn't the be all, end all, or even considered the best representation of gender equality even in the West - many activists back away from using it because Western feminism's current form is still so problematic. It's refusal to challenge itself, it's place in historical and current imperialism and the continual usage of the White woman as universal in theory, practice, and representation (when it's obviously a global minority position). As the quote goes, it's hard to listen to all men being the enemy when our forefathers were killed for looking your foremothers in the eye. I would trust Islamic and Afghanistan's feminists far more on the issue of burkas than a top down approach from Western feminists, particularly if they think they somehow caused the religious conservatism upswing. We should be supporting their work, not talking down and parroting the same quote over and over demonising them.