In order to later diplomatically annex a conquest, one often vassalizes instead of coring. In order to ensure that the vassal (V) has the same religion as the overlord/player (O), one annexes and releases V right after as a vassal (that is, in the war result screen, one does not choose 'vassalize').
An important added benefit is that, by and large, the released V will adopt O's state religion.
However, the change in state religion is not true in the following case: if both the overlord and the vassal are in the same religious group (Sunni and Shia; Catholic and Orthodox; ...), and the overlord is, say, Catholic, but the vassal by nature Orthodox, the released vassal will be orthodox after release.
However again, this last rule is modified as follows: if only the capital of the released V is of O's state religion, then the entire vassal is released as of O's state religion. So you can proceed as follows:
(1) fully annex
(2) convert the capital only
(3) release as vassal with desired religion (and save coring and conversion for all provinces)
My problem: how can you search in game (or even online - I didn't see it in the wiki) what is the capital of a nation? I'm not asking about the crown you see on the top left of the city popup. You need to know what will be the capital of a nation that doesn't even exist yet when you decide which province to convert.
Note also that it is not enough to say "the one province you cannot annex in the war result screen when you don't go for a full annex." Example, you might annex in one war provinces belonging to two future vassals which made up a larger nation.
Sorry for the tldr, but it's a tricky situation I meant to describe fully.
P.S.: One can always load up the start screen and check there; I'm wondering if this can be checked in-game.