I actually have been yelled at and told off in the streets for various mistakes such as this one. And this is not just my personal experience but my German friends also verify such stereotypes.

No, it's pretty accurate in my experience.

DE has strong vigilante culture

FFS, do you even understand that word? DE has the opposite of vigilante culture.

People always rely on some governmental authority. When it affects them, that is. Otherwise, no one gives a shit about anything.

I don't think it's vigilante culture. People value order and organisation and this coupled with the direct nature of communication, feel completely within their right (I would say feel duty bound) to say "hey, you're not supposed to do that".

It is also custom here to voice one's opinion in extreme precision or detail. "Hinterfragen" question things, criticise, always down to the details. Not in an emotional way but very in a very matter-of-fact sense.

So think of it from the perspective of "if the rule is that you don't cross on red, then why are you crossing on red? It's against the rule". It's not personal at all.

Yeah and pedestrians still cross red light I the night fairly regularly.