There are many reasons why stage fright might happen. One that I suspect is very common, is the desire for excellence. Young Sheldon was probably very aware th

There are many reasons why stage fright might happen. One that I suspect is very common, is the desire for excellence. Young Sheldon was probably very aware that he's not the best at communicating complex thoughts to a broad audience due to his unique, or atypical world view. He also had a very high bar of personal excellence and would probably feel like a fool if he exposed himself and failed to meet that bar. There is nuance in "caring about the opinions of strangers". He probably didn't care at all when he was happy about his performance - i.e. it was on them to not understand what he was saying after great thought and probably a very carefully crafted delivery. He probably did care how the others felt when he felt like failed himself by not being up to his own standards.