Okay, I’ll set to one side that phrases like “true for you” (along with “my reality” and such) are among my biggest pet peeves and comment on the body of your post.

“Faith” is an attitude toward certain doctrines, narratives, institutions, figures, practices, and so on, akin to love and trust. And “religion” may likewise describe a set of beliefs (belief in the value or truth of such things as might be objects of faith) or institutions as such which promulgate those beliefs and unite believers.

One could go on at some length distinguishing attitudes one might have, e.g. toward the teachings of Jesus in contrast to the policies of church leaders. A rigorous examination of the latter might even gain support from one’s understanding of the former, as it has in various historical reform movements.

But I suspect that these distinctions would get us sidetracked from what you actually have in mind.

Does faith in a particular doctrine discourage examination of that same doctrine?

What sort of examination? Is everything we might believe to be assessed in the same terms, using the same methods? If not, must we even think in terms of disagreement? Or agreement?

“God sees everything.”

What sort of eye(s) does God have? Does God blink? (Don’t such questions already betray idolatry?) Is God’s sight mediated by electromagnetic radiation and would God’s seeing without in any way obstructing our seeing violate the the law of the conservation of energy? Can we discuss this is scientific terms without talking obvious nonsense?

But is that how such a proposition is properly used? What about:

“God sees everything. So, I will not lead my life as if my misdeeds didn’t matter, so long as no man is there to witness them and I manage to remove all evidence.”

Or:

“God sees everything. So, I will not despair as one who has been completely forsaken, even if I suffer and die, alone and in the dark, and my story is never told.”

These are attitudes and approaches to living that really have nothing to do with science one way or the other.

And surely, a thoughtful questioning of how we are to apply such pictures as “God sees everything” does count as “rigorous examination”. But just as surely, it is indifferent to science.

And such an examination is not discouraged by faith but demanded by it, unless we confuse “faith” with mindless parroting.