I see where you're coming from OP, there really is very little choice.
But speaking as an adult who attended CofE schools, and went to Sunday School and a Christian youth club I can vouch for the fact that it will not damage them AT ALL, being a practicing agnostic myself.
Yes, a young age is an impressionable one, and yes there may be times when you have discussions regarding faith... it is also though an age where you don't decide life long beliefs either and in my opinion, the biggest messages, the ones that stick are the moral stances that I probably share with many religions. Love, peace, respect etc.,
My sons' both attend the only school for miles and it has strong ties with the local church, there is collective worship and the RE element is 'usually' Christian praise... although I do believe state schools should not be associated with any religion and should teach about as many as possible, I do not believe the current system is damaging at all.
My eldest son and I have many theological chats, he asks if God exists, I ask him if he believes, he asks if Santa exists, again I ask him if he believes. The resolution to our talks is usually that different people believe different thing, and if YOU believe then its real enough. He is mad about science and we've discussed things like the Big Bang Theory versus Creationalism, HIS conclusion is that its 'a way of understanding why we are and how we are' that is neither right or wrong, or at least, doesn't matter as we don't know 100% either way.
He asked if we could say grace before a meal, I said we don't do that in our house, but if he wishes to 'give thanks' he can do - so we have our own non Christian grace of giving thanks... for me, its lovely that his Christian influence has made him consider what he eats, his life, his existence, and for that I see it as a good thing, rather than a bad one. I'd say similar if his school had many Muslims in it, or Jews, or pagans etc.,
Its easy to over think this issue, but really, as our children grow they will become more aware of their own beliefs that will possibly differ from our own, or school's. My job as parent is to talk with my child, answer his questions, tell him my own opinion and give him information to find out more.