I mean, I agree that public education generally doesn't intend to indoctrinate children with views that their parents would object to. For one, that'd be nearly impossible to perform in a classroom setting because 30 kids would definitely have parents from a wide variety of backgrounds so you'd have to indoctrinate each with different beliefs individualized to the parents.
I think I'm missing your point here because you seem to not mind the indoctrination that is the basis of having a public education system in the first place, but you started with protesting public education's indoctrination in general, and then when you narrowed it, of course I agree with you because it's never worked that way because it'd be logistically impossible and therefore it most certainly isn't happening right now and therefore unrelated to your original protesting of indoctrination.