The Constitution prohibits Congressional meddling and privileging of one religion over another.
Note that one of the reasons for the 1st Amendment is simple: Some of the states had official religions or dominant religions. My state was originally Catholic, founded by people disadvantaged in Protestant England. This country was not founded on freedom from state-sponsored religion. It was founded on the idea that individual moieties within the federation could each have their own. It was a later amendment pushed that requirement down onto state governments.
It doesn't say that religion has to have the same status that homosexual behavior used to have--best kept behind closed doors, and subject to ridicule and ostracism if displayed in public. For a while when I was in middle school having a Bible visible was grounds for a referral to the principal.
Otherwise, the society--and in a democracy, the government--is most certainly going to reflect prevailing norms. Try telling me there's no taint of state-sponsored religion in having Easter, Christmas, and Thanksgiving as federal holidays. Passover isn't, Day of Atonement isn't, and if I want to take off from my quasi-institutional job for those and for Succoth I use personal days and sick leave, and take a hit to my pay if I get sick or the washing machine floods the laundry room or if my kid's ill. Because some days have greater status than others. (We may say that they're not religious, but they're historically religious and continue, for a lot of people, to be religious. I disapprove of Xmas, personally, but still wind up de facto observing it just like I wound up observing abstinence beliefs by default when I was in a dry county in Tennessee ... before I got hooked up with a moonshine maker, who just happened to be close kin to the sheriff.)
When I taught English in Prague, we started in early July. I felt strange going to work on 7/4, but it was just a regular day. 7/5, I think it was, however, was Cyril and Methodius Day. It was religious, it was historical, it was cultural.
As for imposition, religious dogma and political dogma have, with me, the same status. Both tend to have some close relationship with a set of morals and assumptions of proper behavior. Neither should be foisted on a class of students in the name of "critical thinking" or "doctrinal purity." But neither should divergent views be shamed and the cause of humiliation in the classroom. However, there are still dominant views. A lot of people don't like having dominant views taught. It happens.
I've said before, when I've had to teach things that contradict young-Earth creationism, I've dealt with the matter quickly and have provoked no dissent apart from idiots who insisted on trying to be disruptors. That was to say it was a standard they needed to be familiar with and would be tested over--both the conclusion, the logic, and the underlying facts as known to science. Which was the same for every other standard. No need to believe it, just know and understand it. Because science isn't about belief.
Still, we do live in something like a democracy. If people want to be heard, having even so low-ranking agent of government authority as a school teacher telling them to STFU seems inappropriate. It's their culture, they pay our wages, it's their kids' education.
I also have no problem with a Bible class. I've subbed for them, looked over the assignment and the textbook, and could find nothing denomination-specific in them, nor was it preachy. If I moved to a Muslim-majority country I'd want my kid to take such a class for Islam. Not to convert him, but because so many expressions, so much literature, so much art and so many aspects of the civil and social institutions and culture are connected with Islam.
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