Some portions of the Amish community actually sued Pennsylvania contending that the bright orange triangle required for their buggies violated their moral objection to "decorations" or some such frippery. They lost.
As everyone here knows, the question of the aid going to the students or to the school is a multi-faceted, tough one not easy to sort. Personally, I don't think I have too much objection, but it's not an issue for which I am willing to mount the barricades on one side or another. I do worry about anything that would undercut support for public schools, which educate the vast majority of our young people.
And should a church - whether congregation, synod, district, diocese or denomination - desire to have a school run totally under whatever doctrinal provisions held by that entity, they are free to do so. If someone who does not subscribe to those doctrinal provisions applies for a job there, I have no objection to the school saying "you cannot work here unless...." OTOH, if federal or state money is somehow flowing into that school....
Just teaching that gay marriage is an abomination in the sight of God to be shunned by all faithful believers is not in itself "hate speech." But using state funds to in any way spread that teaching is another problem.
I hope that in considering the future of education, we do not get locked in, hung up, tightly-wrapped or breathless over the "religious freedom" thing. There are more critical issues in education and in the land that need our attention.