Hope there aren't any necrobumping rules around here, this thread in particular caught my attention. Your last activity was in march but, oh well, there might be other people out there that could use this.
First of all, I'm gonna start apologizing if these tips end up not helping at all. I was also diagnosed with GAD, been there, but the way that I deal with it might not be the one best suited for you, vice and versa.
What I usually do is take a deep breath and try to keep close attention to my thoughts, doesn't matter the situation. You might encounter (or have already encountered) people that will take lobbies very seriously and will call you out over the mic if you're a shitty player like me, and it's natural to get nervous over this. Or maybe you're just in a very simple match with some people that seem really nice but still, your extreme self awareness won't let you engage in the conversation. That's when you need to start analyzing your thoughts/feelings. Take some time to think.
1- The cliché "it's only a game" it's overused but it does work. It's not like playing it going to pay your taxes or smth.
2- You're allowed to be a bit self-centered here: it doesn't matter if there are people who take lobbies seriously. It's just a lobby. There are no prizes here, nobody is actually loosing anything besides the 1% lift our egos get when we win a match. Honestly, I like to think of lobbies as just some very organized pubs where you get to play with some really skilled people.
3- Think about yourself and think about the people you're talking to. 1 hour later and nobody will actually remember anything of what happened, so what's wrong in chatting a bit?
4- This one might sound rude but it's not!!! supposed!!! to be!!!! (it actually helps me): nobody cares. I mean, most of the time nobody really cares about who they are taking with or how somebody's voice sound like. Everyone has their own personal lives, with their own personal problems. No one really have the time to think much about some random dude they talked with while playing an online game. People won't pay attention to details as you pay attention to them, keep that in mind.
5- (you can skip this one if english is your main language) To foreigners that get nervous about their accent: if you're able to communicate well enough to your teammates understand you, then try not to worry (read what's written above). And if you ever end up facing someone that will mock your english skills, well, tell them to look for a location restricted lobby or smth. It's the internet, ffs. Full of people from everywhere. Do they live in a bubble or smth? It's 2018. Don't ever feel guilty about being a normal person.
And that's basically it. Again, it's what I do, super sorry if it doesn't help you & sorry for any major english mistakes.