Near me there are many Catholic schools (primary and secondary), Church of Ireland schools (primary and secondary) a Jewish school (secondary) and a Muslim school (primary). Anyone can apply , but their policy is that those that are of the faith of the school have first dips (I may have paraphrased).
As far as I know the only school that doesn't have anyone of any other faith is the Muslin school. This is because more Muslim children living in the area than there are places in the Muslim school, so the places are exhausted before they have got to the end of the list a applicants who are Muslim.
The Church of Ireland is very difficult to get a place at, but you might get one if you apply early enough - this is due to there being a reasonable population of Church of Ireland children and small number of schools.
There's fewer Jewish children than places in the Jewish school, and far fewer catholic children than there are in the area than there are places in the Catholic schools. This means that the list of applicants who are of the faith of the school is exhausted before the places at filled (plus the fact the Jewish school is fee paying!!)
Faith schools are there to educate the children in the ethos of that faith, so why would someone want to go there if they aren't of that said faith? It's because it's a 'good school' isn't it? If it was a 'bad' Catholic school in your area their acceptance policy wouldn't bother you would it?
Here it's actually quite difficult to get into a non faith schools - the overriding majority being Catholic.