Criticism of Churchill, even completely justified criticism, made at this moment contributes to his being fired for uttering unpopular opinions. Anybody making such critiques now bears some responsibility not only for Churchill being fired (if he is) but for the academics who follow them. We don't have academic freedom now, but we have some tattered remnants. I assure you that any left academic who helps destroy what little remains will them when they are gone.
The situation with regard to defense of Churchill's work is not symmetrical, but it still is (in my opinion) a tactical mistake. To defend Churchill's work is to acknowledge that as the primary issue. Though not intended as such, it will be taken as implicit consent to Churchill's continuing employment being based on specific judgment of his work - rather than his status as a tenured professor. On that terrain, if there is not a legitimate major critique to be made, then a legitimate minor one will be found and painted as major. If no minor legitimate flaw exists then one will be invented. Once the concession is made that these are reasons for firing a tenured professor, the specifics can always be improvised. That is the reason the tenure system was instituted in the first place - in spite of the obvious fact some (hopefully small number) of the hateful, the incompetent, the crackpots, and the terminally lazy would be protected by it. Having professors who can take overwhelmingly unpopular positions when they happen to be right is so important that we have found it worthwhile even though the coverage must extend to times when they are wrong.