Do people not want to give autistic people positions of responsibility?

This is the conclusion that Ive come to from years of working/trying to find jobs. When I was in grad school, I was the one of like only two TAs not given their own class to teach. The other person was a girl who admitted to me she has some form of neurodivergence herself. This was despite my near perfect grades, positive recommendations from instructors that I TA's for, etc. Finally, someone told me that they suspect that I am being discriminated against due to autism. They were having first year Master's students teaching but I already received my Master's and was working on PhD.

I have thought of several different jobs that require responsibility: pilot, aircraft control, medical doctor at a hospital, literally anything customer facing, and others. I realized that even if I had the qualifications for those jobs, I doubt I could get them. People will likely think I will show a level of incompetence. I cant imagine being allowed to fly a plane commercially even if I had all the qualifications.

Is this a thing or am I just being pessimistic?

How do I get taken more seriously?