The difference to me is that from a known liar, expecting a higher burden of proof is the only reasonable outcome. Of course, to dismiss all evidence would be wrong but enacting higher standards is only fair.

An anti vaxxer might give good medical advice about a boil that a doctor gave suboptimal advice for, sure that scenario can happen, but absent anything else it’s completely rational to disregard the anti vaxxers advice and follow the doctors instead. The amount of evidence that the anti vaxxer would have to supply is much more intensive than the amount the doctor has to bring before I would flip to the anti vaxxers boil advice.