I have my blackbelt in karate and have a solid exposure to other styles as well, but I think I see what you are focusing on. I wasn't sure what to make of this post until I hit the 'otaku' section of your question/explanation

The was I see it this is a 2-fold issue:

1) Douchebags exist in every organization, group, practice, so on and so forth. With as many styles as there are, and as wide-spread and popular as martial arts are, you are going to have your typical testosterone-driven, grade-A asshole, wannabe alpha males who think they are the best and have a chip on their shoulder about proving it. Something like martial arts will attract these types in bunches, because they focus on the physicality and toughness of it as opposed to the beauty and technique behind it. These are the types who start bar fights for no reason or "someone looked at me wrong" and makes sure everyone they know knows about the fights they start.

2) Some people let a single aspect of their life define their entire identity. Look at some people in the military for example. All of their posts on social media reference or include their service, they get a ton of military ink, they wear "Iraq/Afghanistan veteran" hats with jackets that have the black flag, so on and so forth. Look at some religious people who can't go 5 minutes without weaving their faith into any conversation they have. Look at finance bros who blah blah blah I mean I can list many examples, but I think I sufficiently made this point. The way the martial arts fan or practitioner embodies this mentality and makes martial arts their identity is by acting the way they think the world sees martial arts, and they learned this through (like you mentioned) films, popular shows, books, whatever, and it manifests in an unfortunate way. I'm not a psychologist, psychiatrist, taking psych classes, or anything related to that topic, but I would hazard a guess it stems from insecurity and lack of identity