The biologist Stephen Gould had a theory of non-overlapping magisteria for the truths of science as opposed to religion.
An update of this can be found in Badiou where he posits four sites of not truth but truth-procedures: love, art, politics and science.
Notably and curiously as he is a philosopher, philosophy is missing in this account - but this is simply because he takes philosophy to be dialectic and Socratic; and the clay from which these sites were fashioned.
The logic that ties these sites and their suspension is not classical but intuitive, paraconsistent and progressive (in Whitehead - dynamic).
Notably again religion is missing from this account - and one might remark here that Badiou being explicitly communist has the common communist prejudice against religion; one cannot say because it is not scientific - for art is not scientific either.
One can perhaps locate an additional site for religion fashioned from the other four:
From Love: revelation or unveiling, and the relationship of personal involvement, as in Bubers I-Thou; luminousity and personal transcendence; also community - agape
From Politics: the clearing of space so that it's being can be, sought or defended
From Art: the numinous and the archetype; ritual and tradition; the positing of worlds other than this
From science: scholarship, exegesis, and hermeneutics.
Then religion having its own truth-procedure is neither denied nor affirmed by science (though in some senses it can be).
If this seems rather as though the issue is being ducked; recall the logic that ties these sites including now religion together is paraconsistent and dynamic.