Under some extreme circumstances, religious practices can interfere with the rights of others, or undermine the common good in some other way which allow acceptable restrictions. An example that comes to mind is the ritual use of cannabis, although I do not know where the current line of acceptable use is drawn.
There is a point at which the incendiary communication of religious belief is no longer acceptable; this is now a freedom of speech issue, not of religion. Certain very polemic Islamist-inspired rhetoric can get you in legitimate trouble, for example.
If you avoid those two scenarios, religious beliefs, by themselves, can never interfere with the rights of others.
I find it ironic and troubling that of all the ways one can inform oneself as to how to participate in the democratic process, the very one which is actually protected in the Establishment Clause is the one most likely to elicit complaints of, ‘you can’t use that to inform yourself as to how to participate in the democratic process’. One would think it would be the last reason to be objected to due to such Clause.