American culture .. which you haven't lived. In many places, parents want their religion, not some other religion, taught in public schools (not just parochial schools). Private schools, like your Eton, teach Atheism For Elites (tm). The US is a nation of Hindus ruled by Swedes. In England, it would be as if your Queen decided that yes, she was the head of the Church of England, and anyone not going to Anglican Church every Sunday goes to the Tower. That is what some deluded American want, they want to be English, circa 1640 (theocracy without monarchy).
So if in our legal system, they allow teaching of religion in public school, there is nothing stopping the teachers from teaching Islam too. Parents of course want to have their cake and eat it too, but they aren't the Queen of France. The reason why the public school system doesn't teach religion, even as history ... is because it would we so contentious, that we would break into many mini-states at war with each other, the biggest being Catholic-stan.