“those exceptions are NOT dependent on the nonprofit tax status of the organization.”
In a way, they are. The exemptions only apply to religious organizations, but who decides who qualifies as a religious organization?
The answer, strangely enough, is the IRS. They are the only agency or arm of the Federal government that is specifically tasked with addressing the question. That’s why the Scientologists fought so hard for their IRS tax exemption, because until they had it, they were liable for all sorts of lawsuits on labor laws, etc, that religious organizations are exempt from.
Fair point, though in any case brought under an anti-discrimination law, the court that hears the case would determine whether the religious exemption applies. There’s obviously a risk that the court would look at the IRS determination as dispositive, but it should not (and may not). And, in any event, I don’t think that we, as conservatives, should simply concede that the IRS has that kind of power (as Shapiro seems to concede).