This Atlantic article on the promotion of Christianity in Louisiana public schools is just one example - a topical one at that since we revisit these issues continually in Texas as well. Here's the heart of the dispute:
A federal lawsuit filed last week in Louisiana contains some of the most startling allegations you will ever see against public school officials accused of unlawfully turning their school into a bastion of Christian belief. In western Louisiana's Sabine Parish, one family alleges, teachers preach Creationism and mock the theory of evolution, routinely lead their students in Christian prayer, give extra credit for Christian responses to assignments, and actively question or deride the religious beliefs of non-Christian students and parents.
Presumably all this is done with the consent of the majority, but over the wishes of the minority - which of course has little influence in a majoritarian democracy. A public school is a governing institution and even though these operate on the local level, the 14th Amendment makes First Amendment restrictions created to limit the national governmental power applicable to them as well. This is meant to limit what majorioties can impose upon minorities, but it butts up against a tension that exists in the opening clause of the First Amendment.
While a government cannot establish an official church, neither can it restrict free exercise of religion. The line between the two can get muddled though - and this is where problems start. What's happening in the Louisiana schools is an expression of religious belief, but the fact that it is done in a governing institution - a single purpose government - with the authority of the board and administration makes it seem like the religious expression becomes the official "established" one in the institution.
Those who do not adhere to it are seemingly treated in a secondary manner. Which leads to the constitutional conflict.