Social anxiety disorder, yes. Aspergers, absolutely not.
It's possible in 24th century personality disorders are now just accepted as 'Who the person is' and not categorized disorders.
If humanity has progressed so much, it's probably progressed beyond pathologizing every personality trait which isn't adaptive to the norm, and started just accepting people for who they are.
social anxiety disorder isn't characterized as a disorder because it's different from the norm, it's characterized as such because it significantly disrupts a person's social interactions, and has a negative impact on their life as far as dating, friends, employment, etc.
Introvert is a personality type, but "socially anxious" is not, because the person with SAD often doesn't WANT the anxiety associated with typical social interactions.