That would depend on whether the private school was explicit about it's programme when students were enrolled. If a school were to bill itself as a "communist" school or a "christian" school, and made it clear in its literature and in interviews with prospective students and their parents that that point of view would be taught, then I would not have a problem with it. If the private school billed itself as nonsectarian and nonideological (as most of the better prep schools do), then I have an issue with indoctrination.
For the most part, my point applies primariliy to state supported schools. My personal view is that teachers generally should assist students in learning to think for themselves, rather than inculcate a particular ideology, but I would not restrict the right of those who disagree to offer private ideologically-based instruction assuming they are candid about what they are doing.