Well, the problem is rooted in the origins of the Constitution and the republic itself. For one thing, the general assumption was that everyone (who mattered, or should matter) believed in God, and moreover that “religion” meant “some form of (probably Protestant) Christianity,” at least nominally. The danger they saw was the sort that had bedeviled the European Christian world since the Reformation, namely the persecution of one sect by another, and the establishment or continuance of state religious establishments.
They did not conceive of a society where any form of total non-belief was normalized. American thinkers well into the 19th century, and beyond, opined regularly about the indispensability of morality and a sense of virtue grounded in a belief in God, always defined in a very Christian and usually Protestant fashion. Even other believers, who were not Christian, were pretty much beyond the pale in terms of how folks thought about protecting the right of religion. Jews were sort of grandfathered in, but they were not thinking “hey, we should make sure all Muslims and Sikhs and Buddhists are protected!”
Essentially, the Founders wrote religion into the Constitution in the way the 1st Amendment was interpreted and in the way the whole document is actually written. Like other American documents, the rhetoric is decidedly Christian in much of its tone and vocabulary. One was guaranteed freedom of religion, with the clear assumption that you were expected to HAVE a religion. The state was prohibited from ramming its version of religion down your throat, with the assumption that it wouldn’t have to because you would be following your own faith, one that was assumed to be within the general ballpark of generic Protestantism interpreted broadly.
Fast forward to today, when we rightly interpret religious freedom as also including the right to not be religious. We also understand that the implicit limitations of that right to just Christianity that was part of the original intent no longer applies, and that freedom means freedom for any religion (though defining such can be tough). Our laws, though, have already clearly established religious institutions as having special protections, while non believers, not having any institutions per se, of course have not gained anything like the exemptions from taxation or labor rules that religious institutions receive. For the Court to rule that religious institutions (and the ones most often bringing cases to the Court are invariably Christian) are subject to the same laws as everyone else would effectively mean the rejection of a whole corpus of law and the establishment of a meaning of “separation of church and state,” which was at its origin quite narrow, that would be very far-reaching. It would in effect mean that the country takes a default stand of “no preference” on the issue of being religious or not being religious, instead of taking that stand in regards to which religion one practices.
FWIW, I think such a shift is long overdue. To the modern mind, many of us anyhow, the spirit of the 1st Amendment requires the government to get out of the religion business totally, including tax breaks (unless those breaks are extended to other community groups without specifically religious character) and any labor law exemptions.
That being said, I don’t in general see much issue with, say, a Catholic school insisting you don’t contradict Church doctrine in your classes. I’m even open to discussions about allowing such a school to require employees to be practicing Catholics, as long as the school doesn’t get any federal money. The health car stuff is more bonkers, for sure.
