Here is a fairly good overview of what transpired.  FAU's stated rationale for termination–failure to file reports about his "outside activites"–seems feeble and implausible.  What they should have argued is that, given his academic specialty, his conspiracy-mongering suggests professional incompetence–it would be as if a biology professor taught creationism instead of evolution by natural selection, or an astronomy professor taught that heliocentrism was false.  This process would have taken longer, but the fired professor's grounds for a breach of contract suit are probably stronger given how the university actually went about terminating him.