I encounter this fallacy frequently in online discussions where an opponent completely disregards all of my premises and says my conclusion is invalid because it's an "opinion" and "not objective."
This is not merely questioning the bias of my sources: the opponent often makes no attempt to refute my premises. In extreme cases, they argue that only a 100% objective argument can be valid. I had this happen even in debates involving game design, visual design, or other disciplines/topics requiring subjective judgment.
I know from my critical thinking class that this is a fallacy because debates (by their nature) can be described as a clash of formulated opinions. But does this have a name?