The consensus out there is that approach anxiety comes from evolution/how ancient societies used to be: you're in a small tribe where there's a handful of attractive women. If you hit on one of them, it could either mean death or you'll never pass your genes, so we're genetically wired to have approach anxiety.

I disagree. I think approach anxiety comes from Elementary School and early childhood conditioning. Think about it: you're in an elementary school where you literally know everyone and if you do anything embarrassing, your whole grade knows. This is traumatic. No genetics necessary here. Approach anxiety comes from early childhood/school conditioning. And this is good news, because it's a lot easier to undo THAT conditioning than literal genetics.