"Hey wanna come over to a BBQ at our place on Saturday?" might be awkward for a vegan to respond to, just as "Hey, wanna come over for spaghetti night?" would be for someone on a low-carb diet without any specific disrespect or disapproval from the host about the particular diet. I'm assuming you wouldn't recommend telling someone to "fuck off" for inviting you to a BBQ.
That's what my original post was about. None of that stuff even matters. It's cliche to say but it's only awkward if you don't have true self-acceptance, THAT is what makes it awkward. Otherwise, its your reality against theirs, and if you bend to their reality it's basically telling your own self "that person's beliefs are more important than my own"
If someone invites me to a BBQ I would just eat beforehand and then come over and socialize, have some water or carrots/hummus (if they have it), or nothing at all. If someone asked why I'm not eating I would just say I'm vegan (if they didn't already know) and I already ate for today. Anything beyond that conversation (i.e. making sarcastic jokes) I'm used to, I'd play along with it. There are rare times where the jokes get too much in which case I 100% ignore them so they get the idea that they should chill. Looking at people in the eye as they're talking, and then slowly looking away while they're mid sentence is a really good indicator that "ok... that's enough" without having to talk about it.
For all the quarterly meetings at my old job, we would go to steak houses every single trip. The amount of times I've heard a waiter/waitress say something to the effect of "You're at a steakhouse pussy, you want a salad???" ... I dunno it just doesn't phase me. If they're a huge asshole I will be an asshole back... "Yeah did I stutter", but this is quite rare and usually only at really meat-centric places like Brazilian steakhouses etc. One memory I have was at this famous BBQ place in a basement in Memphis. He called 3 or 4 people around to have a 30 second comedy show at my expense, but I played along with it and shot remarks back, after which we all laughed and I ordered a water and a thing of potato salad.
99% of the time though, no one even cares, and people are polite.
Not to mention the self reinforcing effects of social pressure - for example, if you're a vegan and you want to go out to eat with your friends, your options may likely be limited depending on the restaurant. If your friend group is considerate, they may take vegan options into account, or you might end up going out less with your friends as a result.