Secular humanism not being a religion, does have a set of beliefs. It would seem unconstitutional if someone had to pay a teacher to teach my kids the Bible, or the Quran, and many things taught in government schools are counter to beliefs of religion.
I don’t see a solution to the problem that doesn’t cause crazy amounts of abuse other than the government completely gets out of education, or local communities/governments alone support it and the school matches the beliefs of the local community.
None of that seems plausible. So how do you respect the 1st amendment rights of people like the article talks about?