Can you describe a general situation where this kind of skepticism is avoided? I'm keenly aware that selective application of standards of evidence in legal matters is a serious bias problem, but if you are suggesting it happens in some issue to people across the ideological spectrum on that issue I don't know what you're talking about.
Skepticism and comments about skepticism don't necessarily need a linear relationship. Making a pro skepticism comment is a reactionary move against people treating anonymous accusations as fact. If you see more people doing the latter when racial or gender discrimination issues are discussed then it makes sense that the former will follow.
The more serious/terrible the accusation, the more likely it seems to me that people will just take it on face value.