What careers can one speak about divisive topics, and not get in trouble?

“news” anchor or talking head.

Polemicist.

I agree with tenured professor, as I am one. That said, I teach graphic design, which is never really controversial. I really wouldn’t want to test the theory if I were a political science, criminal justice, or even psychology professor.

Sociology.

edited

Mathematician .
I know a guy who is the most obnoxious, conceited, opinionated person known to man. (He is single and will be forever.) But, he is a brilliant mathematician and can figure out anything.
Give him an impossible problem and send him away. He will come back in 2 days or a week with a solution. And it will work!