Actually you're factually wrong about Islam. It's been a cardinal point of the Sunni sects (which are 90% of the world's 1 billion Muslims) that as in Protestantism there is no priesthood or clergy to arbitrate belief and that all Muslims are equal in that sense, be they man, woman, rich, poor, or what have you.

And also the religions do not radically overhaul their doctrines so much as they adjust to the modern world.

Tell me, is eugenics really a science or isn't it? It had peer review, experiments, and a full-fledged apparatus to study it. So is it or isn't it, or like religion does science fall in and out of favor in conjunction with politics and society as a whole? Was eugenics and is eugenics still a science or was it simply rejected because the Nazis took it to its logical conclusions?