I also find it stressful to make small talk or socialize when eating. It's also hard to just sit near strangers when eating even if our backs are turned. I feel my space is invaded and a certain pressure that the other people are expecting something from me socially.
I have learned often when I am uncomfortable to go ahead and change the situation. I might take the last roll and juice box and finish on a bench outside. If I had to eat in a cafeteria where people pile in, I might start getting it in a take out box and find a bench by a tree that is "my" little spot for lunching. One good thing is that if you just smile at people in a friendly, supportive way, it is easier to make these adjustments without being perceived as snubbing or rude. And if you think about it, a person has a right to their space and it doesn't have to be unkind to the other people. I usually feel okay doing these things because I don't dislike the people, I just know I need my space. It is partly what helps me like people in general. I try to create the boundaries I need to be comfortable as myself, so no hostility builds up towards anyone. It can be okay to leave.
One thing difficult for me are required meetings for work where there are a lot of people in a small space and everyone is talking excitedly and loudly. It is like sensory overload especially if there are a lot of emotions being expressed. I tend to perceive too much of the emotions expressed around me and it takes a while to process, so besides the sensory overload, it is also an emotional overload. I have tried to explain it to people - it's almost like having bright spotlights and sirens everywhere, but the emotional equivalent. It's disconcerting. I usually take breaks and go outside and make a call on my cell phone or pretend to just to regain my bearings. I've read someplace that introverts tend to take in more without filters, and it takes longer to process and sort it all out whereas the extrovert filters things as they go and so they don't end up with the same feelings of overload. I think needing space is related to feelings of overload and that is why introverts need it.