It is a real shame. FIRE's heart is in the right place, but their thinking is terribly confused. They seem to think that the problem with diversity of speech, expression, research and assembly on campuses has something to do with the "adjunctification" of university faculty.. And they seem to look to tenure as a way to fix this.
For a private university one may wonder about the applicability of the 1st amendment anyway. There is no 1st amendment freedom in my private house or my private business, why would there be in a private college? It is a matter of private property rights. One may, I suppose, argue that if the university receives public money it becomes a public space that attenuates private property rights. And this, again I suppose, is the argument regarding public universities. (Though many are very "mixed" spaces).
The public nature of many schools is a problem in a different way in that its administration and faculty may get "captured" by social and political interest groups who then pursue a particular agenda and penalize those opposed to it. This is indeed the case throughout academia. But, it has little, if anything to do with tenure. And, clearly, as we are seeing, tenure is not a solution to this iniquitous bias.
FWIW, I think tenure is a terrible institution. I think organizations should have the right to hire and fire (not renew) whomever they like. I think the problem lies in the faulty missions of universities not in their authority to determine who works in them.