...true beliefs that will have negative signaling consequences or drastically reduce one's happiness.

Do you have some examples of such beliefs?

Here's a good example: "The paper that supports the conventional wisdom is Jensen, A. R., & Reynolds, C. R. (1983). It finds that females have a 101.41 mean IQ with a 13.55 standard deviation versus males that have a 103.08 mean IQ with a 14.54 standard deviation."

Now, people will lynch you for that difference of 1.67 IQ points (1.63 %), unless you make excuses for some kind of bias or experimental error. For one thing, the overall average IQ is supposed to be 100. Also some studies have females with the higher IQ.

But what about that other bit, the 7% difference in standard deviation? Stated like this, it is largely inoffensive because people who know enough math to understand what it means, usually know to disregard slight statistical variations in the face of specific evidence. But what if you take that to its logical conclusions concerning the male/female ratio of the top 0.1% smartest people, and then tell other people your calculated ratio? (to make sure it is a true belief, state it as "this study, plus this calculation, results in...") If you state such a belief, people will take it as a signal that you would consider maleness to be evidence of being qualified. And, since people are bad at math and will gladly follow a good cause regardless of truth, almost no one will care that looking at actual qualifications is necessarily going to swamp any effects from statistics, nor will they care whether it is supported by a scientific study (weren't those authors both males?). And the good cause people aren't even wrong -- considering that people are bad at math, and there is discrimination against women, knowledge of that study will likely increase discrimination, either through ignorance or intentional abuse -- regardless of whether the study was accurate.

If you accept the above belief, but decide letting others know about your belief is a bad idea, then you still have to spend some amount of effort guarding least you let slip your secret in your speech or actions. And odds are, such a belief would provide you zero benefits while exposing you to a small but constant loss of mental resources and a risk of social catastrophe.