No, they shouldn't, and I'll follow-up as to why below.
>Very quickly, the proposal that the moon is made of Vince Foster would be dismissed as false. This is critical thinking in action.
Given sufficient rhetorical skill and sufficiently many appeals to "open thought" or "questioning assumptions" or "viewpoint diversity" - in short, various forms of postmodern denial of the external world and the strict rules for reasoning about it - a sufficiently motivated student or professor will manage to make "the moon is made of Vince Foster" the center of attention.
We are living in the same world, with the same academic institutions, which was fooled by the Sokal Hoax, and we are also dealing with the human psychology of social proof, in which giving time and energy to considering an idea in-detail is considered evidence for the idea's truth (rather than evidence for its vagueness or logical complexity).
We cannot allow academia to be consumed with discussions over whether gravity is a social construction, especially not because right-wing partisans feel that only mostly owning the field of economics means that academia is engaged in conspiracy against them.