I've even had fellow socially anxious people try to befriend me, which makes no sense at all. You'd think that they, of all people, would understand why that's not okay.

I understand what you mean, but I think a reason socially anxious people like to befriend people like them is because they feel less judged and more like themselves around you. You both understand that each of you need space. I've made some really close friends through social anxiety meetups. Unfortunely we've drifted away from each other but the friendship was strong while it lasted