Bad faith and 'just asking questions'

There's a certain kind of question that raises suspicion as to the motives of the person asking it. 'Was the Holocaust really as bad as historians have made out?' 'Is there really a scientific consensus on climate change?' 'How do we now for sure that vaccines aren't harmful?' These kinds of questions can be read on the surface as innocent enquiry, but sometimes they can function as a kind of epistemic sabotage, casting doubt on settled issues and seeking to undermine confidence in established truth. How can we tell the difference between sincerity and bad faith? And how should we respond to the latter?