The thing is though spicemonster, faith schools ARE generally divided along racial lines.
Show me a black catholic. I know they exist, but I've never met one.
Show me a black jew. I know they exist and I have met one in Israel, but there are not very many of them.
Show me a white muslim. I know they exist but I have never met one.
So in fact, by drawing lines around faith, in de facto terms, the schools are also drawing lines around race as well.