I can see there being a few different levels here.
Knowledge of the existence of Heresy is widespread, and the basis of population control on many worlds. In the absence of widespread education, then rumour and superstition will be rife across all human worlds which will assist in generally supporting hunting down heretics, but will probably really muddy the information water on the exact nature of chaos. There is a pretty low bar in the background for mutants to start cropping up as well, so everyone will be on the watch for "twists", and generally "knowing" that they are bad.
Similarly, that fact that individuals can "do magic stuff" must be well known and all citizens are empowered to inform to the relevant authorities about any such occurrences.
However, the specific nature of Chaos, how it works and the details of each of the 4 main gods will be less well known. This is supported by the position set out in the Cain books regarding knowledge of Imperial senior Guard staff.
The trigger for mindwipe can be hand-waved as relying on some very specific things happening. For example, in the Tanith books, they find themselves fighting across blasted wastelands with chaotic runes actively corrupting troopers and weird magical stuff happening regularly, and whole regiments are not purged for that reason. However, for maximum grimdark impact, there are cases where whole battlegroups are purged for some related reason. I imagine its also similar to exterminatus. Theoretically any Inquisitor can call for one, but they might not have the political clout to actually get the operation started. /Same with mindwipe and execution of witnesses. Poor old Blue squad who's 8 members happened to see the wrong thing, easy. 34th combined army group consisting of 1,000,000 men, responsible for holding a critical location against imminent attack, harder.
Similarly, I imagine that anyone with a general knowledge of Inquisitorial Ordos will understand that Ordos Malleus has a Chamber Militant. Exactly who those troops are, and the details of their base, training, make-up and equipment, will be more secret.
Very few people in the 40k universe will ever see a space marine, let alone a Grey knight. As long as people on relevant missions aren't going around announcing who they are and exactly what they are doing, most witnesses will just see big chunky bois smashing the bad guys really hard, hooray!
I would imagine that the High Lords would know most of these things in concept.
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