It is a coincidence that I happened upon this from Volokh’s blog, but it’s illustrative of what happens when you ignore the separation:
The free, equal, and undisturbed enjoyment of religious opinion, whatever it may be, and free and decent discussions on any religious subject, is granted and secured; but to revile, with malicious and blasphemous contempt, the religion professed by almost the whole community, is an abuse of that right. Nor are we bound, by any expressions in the constitution, as some have strangely supposed, either not to punish at all, or to punish indiscriminately the like attacks upon the religion of Mahomet or of the Grand Lama; and for this plain reason, that the case assumes that we are a Christian people, and the morality of the country is deeply ingrafted upon Christianity, and not upon the doctrines or worship of those imposters.