If it turned out that a paper was using fudged data, or the results were measured poorly, or that the math being used to crunch something was incorrect, I would like to think that I would be willing to readjust my position on it and go where the latest research points. Einstein proved that Newton's "laws" of physics were really just really good approximations, and I think the vast majority of physicists were willing to adjust accordingly.
If it turned out tomorrow that Type Theory was shown to be unsound or something, I'm pretty sure I'd just concede that I was wrong to believe it, and then move onto whatever revised framework came along to replace it. I wouldn't just tune out all contrary perspectives and vehemently insist that "no type theory is always right and I have faith!!!"
So you're right; it's not equivalent to religious faith, because religious faith typically involves readjusting your perception of the world to fit with it, while "faith" in science involves changing the data to fit better with the world.