What does this mean?
"in the classical world" means people who are involved in classical music, in this case. "People in the programming world" would refer to people involved in programming.
"taking a political stance" means to have a political belief.
"they might", in this case, means "maybe they should" or just "they should". You could say "you might put a lid on your coffee cup" to somebody that does not have a lid on their coffee cup, but you think that they should. You can imagine some missing words, like "they might (if they were smart) at least worry...".
"at least" means "if nothing else" or "if you just do one thing, do this".
Another version of the sentence could be: "People who work in classical music should not want to appear stupid, even if they are not interested in politics."