Are you or are you not free to choose your child's private education?
If fact it is cognitively, intellectually, socially and politically impossible to have "freedom from religion,"
Our entire internal world, our civilization and our political foundations are deeply shaped and informed by it. Too suggest otherwise is just preposterous, and a thoroughly narcissistic and solipsistic understanding of what civilization is, or what the human is.
Likewise you notion of "choosing your children's private education is both spurious and specious.
1) Why should parents be forced to withdraw from public schools rather than decide to change them? Are the not coerced in to supporting them? Are they mere serf? hardly seems democratic or "public" to me.
2) There are no value neutral curriculum - they do not exist in a vacuum. Some group of people decide these things, and that group promotes its own believes and agenda. It is intellectually dishonest to suggest otjherwise, and it is arrogant for you to imagine that you have the right to foist your believe system on others without any political form or political outcome.
3) Secular humanism and Socialism are really just other belief systems and apply a quasi-supernatural mandate to their core beliefs as well. "Socialist man," Scientific materialism, "Scientism" or even the efficacy of reason as an ultimate moral arbiter are no less mystical or religious assertions than a belief in the Virgin Mary, and a great deal more harmful, I might add. Nothing could be clearer from the history of the 20th century.
4) In principle, no, parents cannot chose if there are economic. geographic or logistical limitations placed on them. This is a particularly specious formulation, and for obvious reasons.
5) You assume that your position is the majority position birth nationally and regionally. I fail to see how this is so.
So, based on what you have articulated, I find you position faulty in its whole and its parts, and not a serious position whatsoever.