I went to a private school. I am here to tell you that the only time there was any "faith based" based teaching was during the religion class.
All other subjects were taught based on the science of the subject!
I have never advocated for faith based teaching. To assert so is to introduce your own personal bias into the discussion. Please try to refrain from doing so as I make effort to be specific in what I say.
I will give credit for you apparent acceptance of various students differing desires, "I have no problems with religious clubs at school".