The parents of those children are also taxpayers, so are already contributing towards the school. I know the church partially funds these schools, but don't know by how much currently.
If you allow all children over every faith and no faith to attend a Catholic school equally, and I can see the argument, then they cease to become Catholic schools because the parents would not have any interest in faith.religious activities/events/teachings etc.
I'll be honest, I'm a very lapsed Catholic, and on my divorce wanted my son to go to the same Catholic school that I did which had an excellent reputation and brilliant results. He was already baptised or both sets of devout Catholic parents would have murdered us ironically.
I moved back into the area, and having a then 2 year old, (25 now) his choice of school was a major factor in where I moved to.
But I was brought up in that faith, and could support my son in that faith until he was old enough to make his own mind up. Then he lapsed too.
But overall I think what I am saying is despite my own behaviour faith schools should be available for people who want to bring those children up in that faith as a priority. Their parents are taxpayers too.