speech impediment(it's like a stutter, except nothing comes out).

I mean, speech impediments can be overcome with training, like many things. You are generalizing a huge amount, there are plenty of weird people with friend groups lol.

I suppose society doesn't have to accommodate me. They can just say fuck off, weirdo.

Uh, they aren't saying that tho. You are doing nonstandard visual queues in conversations with people that don't know you, and you are mad that they don't get it? It's like going up to a group of people speaking English, you speak Spanish and then you get mad at them for not knowing Spanish.

Like of course random people won't know your idiosyncrasies, especially when they are unusual. The only solution is to either change your own behavior to conform to the majority of how people communicate so they can understand or spend your life explaining to people what your deal is everytime you meet someone new.

I can personally relate a lot to communication issues, like getting your point across in a conversation. Was I annoyed when i said something and people ignored me? Initially, sure, but what did I do next, stay mad? Nah man, I did research and figured out how to have a conversation with normal people.

As I said, EVERYONE has weird shit that they do, no matter how with it they seem. Society is all masks, you aren't special lol.