Well, socialism is about wanting the means of production to be owned by the community at large. I think you can believe in that, and yet at the same time recognise the limitations of the world as it currently exists. I don't think there's anything particularly socialist about refusing to buy a house in the catchment area of a good school, for instance.
I do think private education is pretty much a no-no.
Faith schools - not particularly unsocialist, I think? I mean, this is socialism, not communism - there's a fine tradition of Christian socialism.
Tory - well, you could vote Tory if they were advocating socialist principles. I briefly thought about voting Tory when Michael Howard talked about wages for housework.