It's so common to see people here straight up stating their headcanon as fact. I don't know whether they're lying on purpose to try to make their headcanon get traction with people who don't know any better which means they're trying to prey on ignorance, or whether they're so delusional they believe it themselves.
Enough faith in the Emperor does in fact make you immune to chaos. If your faith is strong enough, you can walk through a nurgle plague without so much as a runny nose, or you can see right through a tzeentch deamon's mirror image and simply shoot the correct one because illusions don't work on you. The reason these sorts of things work on most people is because most people don't have the level of faith required to overcome them. Your average random guardsman is going to turn into a zombie or shoot wildly. But someone who believes in the Emperor simply trusts that He will guide your hand, and sure enough, you aimed at the right mirror image, or you believed that the plague won't affect you because the Emperor's will is stronger than Nurlge's plague. It actually works, because faith is real in 40k, and the stronger you believe, the better it works.
This is the foundation of the SoB's supernatural element. It's represented on tabletop by acts of faith, and the army wide 6+ invuln save represents the lore that some sisters' faith is so strong, it literally bends bullets away from vital organs because she just believed so strongly that the Emperor would do that for her. When you pop an act of faith to gain more shots or ignore cover or these gameplay effects, that's literally a manifestation of their faith bending reality, because the Emperor is that powerful.
So no, it's not true that "it's actually common for SoB to fall, they just cover it up", it's not true that SoB fall to khorne so often they're "known for it". Absolute bullshit lies and headcanon. I've read every SoB related book and I play the army.