More a question of indoctrination rather than academic demands.
Coming from New York City as I do, I can tell you that PC was alive and well 40 years ago (though not called that).
There is certainly that aspect to consider when comparing public vs. private schooling, and it is a major one. At the pre-k and kindergarten level, though, I think it is less of a factor. We are mostly talking about things like letter recognition, colors, shapes, tying shoelaces, etc. The real indoctrination into all the PC crap doesn't start until a few years later.
The major difference between public and private (religious) pre-schools is that in the church based schools, such as my wife's they do get some religious education; read Bible stories, sing hymns, etc.