I can't answer for the situation in the US but in Australia it's very common to send children to either a private or independent religious school (the vast majority of private and independent schools here are faith based) without having any affiliation with that faith. I personally know quite a large number of parents that have done this with no adverse consequences. As JDAx3 has stated, in most cases it isn't an issue as long as the fees are paid, keeping in mind that the children are expected to practice and participate in the fundamentals of the given religion, at least during school hours.
I understand where you're coming from and from a personal perspective I would ask myself this question, and most likely other parents (carefully chosen so as not to offend), amongst all the others.
