All the kids ARE singing non-Christian songs in the public schools these days.
The 1st Amendment bars the state from establishing a religion. It makes sense that kids should not sing religious songs in school.
To impose a religious belief on children who do not belong to that religion is wrong.
To use the mechanisms of the state to require children to sing Christmas songs is unconstitutional and wrong.
To teach children about religions, in anything other than a historical or anthropological sense, is unconstitutional and wrong.
There are also
plenty of opportunities for people to teach their kids about religions,
and to express religious beliefs in the public square.
Meanwhile, Christianity has a long history of intolerance. Even in its earliest days, there was conflict over the interpretations of Christ that lasted centuries, whether it be James and Paul disagreeing, to numerous Gnostic interpretations, to feuds over the nature of the Trinity resulting in theologians condemning one another, to Irenaeus' attempts to purge the Church of "heretics." Constantine's demand that Christianity cohere into a single theology (at the First Council of Nicaea) is an expression of a refusal to allow theological diversity. This continued with centuries of persecuting Jews, Pagans and other non-Christians, to wars with Muslims, to invading Judea in the Crusades, to sectarian violence throughout Europe, to Puritan colonies outlawing all other religions and Christian sects, to anti-semitism and anti-Catholicism running rampant right through to the 1960s.
Religious liberty basically came to the fore in the early United States, because some of the earlier intolerant groups (like the Puritans) were starting to get outnumbered and outinfluenced by other sects, such as Anglicans in the 1750s. Even the colonies that instantiated religious liberties (like NY, PA, RI, DE) limited their official tolerance to Christian sects.
Not all of this was exclusively about religion. Not every single Christian, or Christian community, or Christian theologian, were intolerant. But it was not Christian theology itself that dictated tolerance in the early United States. It was political conditions, combined with Enlightenment ideals about human rights, which brought about that shift. There is no historical reason whatsoever to attribute religious liberty or tolerance to Christianity or Christian theology.