No, NHS hospitals which gave priority to Christians would not be acceptable. However, the parallel is not an exact one - there is no branch of Christian medicine that I am aware of, so there is nothing that a Christian hospital could provide that any other hospital could provide. Also, all hospitals that are not private are state founded and funded - there is no equivalent in hospital terms that I am aware of, where religious groups set up their own hospitals for their own faith members. And then pay extra charges for the specifically 'religious' medicine.
I suppose there is a (slightly inexact) parallel in that you can pay extra to be treated at an NHS hospital by NHS doctors or go privately for some or all of your treatment. Thus when I had my dcs, I could have paid extra for a private room - much nicer than I enjoyed in the open ward.
That is how the NHS works - you might not like it, but people can pay extra for extra treatment or perks. Obviously this is based on wealth not religion, though - but there is no more inherent logic in it. It is using buildings built and doctors trained by the state.
I think your objection to faith schools would be more rational if pupils at those schools were getting an inherently superior education. But they're not - they are getting an identical secular education. The only bit that is different is the specifically religious ed - which they pay for. And which I assume you wouldn't want anyway. Children from faith backgrounds need to be educated SOMEwhere - so they set up their own schools for this purpose. Which you now want to appropriate after they have done all the hard work and put up the cash, rather than setting up your own schools.
Do you not realise that if they hadn't set up those schools, there would be LESS schools, and non-denominational schools would be even more overcrowded, and it would be even harder for your children to get a place there? The state would then have to pay to set up more schools, instead of them being subsidised by churches etc. And that's if they bothered to - this thread suggests that they are not likely to have much help from the secularists and humanists, who are all too 'busy working'.