There was a comment above about how tenure is being "dangled like a carrot" in trying to censor the professor. I think that this is a bad misreading of the scenario, and let me try to give my prespective as a professor who is (hopefully!) also on the way to tenure.
First, note that in the quote you use, the mentor was not telling Prof. Gil-White not to publish on a certain topic or not to write letters to a publication, anything like that. The advice was given to not speak about a certain subject in a course. This is honestly a completely different issue.
Ok, maybe I'm lucky because I am in mathematics, and therefore I never have to bring any controversial material into the classroom. This guy may have to make more borderline decisions. That being said, I think that one should minimize the controversy in the classroom before one is tenured. Tenure is a serious decision which is not taken lightly by any school, and controversy doesn't really help.
Second, I really think that this guy's mentor is giving him advice which is good and heartfelt. I would probably do the same in a similar situation. You might make a reasonable argument that the advice is wrong, but it in no way is anything like censorship. He's not telling him not to publish, he's telling him what he should say "in front of the kids", which is really another ballgame altogether.
Third, remember the function of tenure: one can do controversial work and not worry about repercussions, and this is the source of academic freedom. But you gotta get there. The best way to do that is establish a research identity of a consistently solid scholar. Controversy is probably not be the best way to do this.
Damn you and your daily doubles, you brigand!