I used to teach in a catholic school and probably 30% of the kids came from catholic families, of which about 15% were actually practising catholics.
The rest of the kids were either Cof E or of no religious background. Most of the parents chose to send their kids there because the classes were small (17-20 kids max, as opposed to 30-33 in the other schools in the town). Priority was given to (practising) catholics but if it hadn't taken non-catholics then it wouldn't have stayed open.
School funding is mainly based on pupil numbers so it wouldn't have been in their interest to exclude non-catholics.
Although the curriculum was slightly more heavily weighted towards RE and we had mass 3 times a term, as a non catholic, I don't think my classes got any more of a 'religious' education than they would have done in a non-catholic school.
The other point I was going to make, is that of 7 teachers and the head, only the head was a practising catholic, the rest were either Cof E or fairly agnostic/apathetic. There just aren't enough practising catholics around here to sustain a purely catholic school.
TBH, apart from the presence of a few religious icons, I didn't really find the whole experience of working there much different to jobs I'd had in non-religious schools. I don't really have any strong feelings either way as to the rights or wrongs of the state funding religious schools. At the end of the day, central government dictates pretty much what LEA funded schools have to teach, right down to lesson timings and content and all schools, religious or not have to abide by it or they have OFSTED to answer to.