<So the far left needs to be excluded from certain professions. Any other groups you want to add to your blacklist?

Sure. Loads of them.

Nazis should not be hired as teachers.

Child molesters should not work at day care centers.

Radical environmentalists should not work in nuke plants.

Radical Islamists should not be put in charge at a water treatment plant.

I could add a lot of others whose beliefs ought to keep them out of certain professions, and I'm sure you could think of a few too, but this is just off the top of my head. I do NOT advocate the government passing any specific laws to this effect. What I do advocate is raising the awareness of the people who do the hiring--such as university administrations--to the point where such people are just not hired any more.

If the beliefs of a professor are demonstrably wrong, it is stupid to hire that person. Would you hire a chemistry teacher who believed in phlogiston? A flat-earther teaching astronomy? A fundamental creationist teaching paleontology?

There is no reason a university administration should treat an avowed Marxist any differently than an avowed white supremacist. Neither should be teaching students.