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HughRistik comments on Making your explicit reasoning trustworthy - Less Wrong
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Do you have some examples of such beliefs?
The problem with the most poignant examples is that it's impossible to find beliefs that signal low status and/or disreputability in the modern mainstream society, and are also uncontroversially true. The mention of any concrete belief that is, to the best of my knowledge, both true and disreputable will likely lead to a dispute over whether it's really true. Yet, claiming that there are no such beliefs at all is a very strong assertion, especially considering that nobody could deny that this would constitute a historically unprecedented state of affairs.
To avoid getting into such disputes, I'll give only two weaker and (hopefully) uncontroversial examples.
As one example, many people have unrealistic idealized views of some important persons in their lives -- their parents, for example, or significant others. If they subject these views to rational scrutiny, and perhaps also embark on fact-finding missions about these persons' embarrassing past mistakes and personal failings, their new opinions will likely be more accurate, but it may make them much unhappier, and possibly also shatter their relationships, with all sorts of potential awful consequences. This seems like a clear and realistic example where less accurate beliefs are in the best interest of everyone involved.
Or, to take another example, the post mentions people who expend some effort to follow certain forms of religious observance. For many people in various religious and ethnic groups, such behavior produces pleasant feelings of one's own virtuousness, as well as positive signals to others that one is a committed, virtuous, and respectable member of the community, with all sorts of advantages that follow from that. Now, if such a person scrutinizes the beliefs on which this behavior is based, and concludes that they're just superstitious nonsense, they will be forced to choose between the onerous and depressing burden of maintaining a dishonest facade or abandoning their observance and facing awful social consequences. I don't see how this can be possibly seen as beneficial, even though it would mean that their beliefs would become closer to reality.
This is a good point. Most ideas that are mistreated by modern mainstream society are not obviously true. Rather, they are treated as much less probable than a less-biased assessment would estimate. This tendency leads to many ideas being given a probability of 0%, when they really deserve a probability of 40-60% based on the current evidence. This is consistent with your experience (and mine) of examining various controversies and being unable to tell which positions are actually correct, based on the current evidence.
The psychology seems to combine a binary view of truth combined with raising the burden of proof for low status beliefs: people are allowed to "round-down" or even floor their subjective probabilities for undesirable beliefs. Any probability less than 50% (or 90%, in some discussions) can be treated the same.
Unfortunately, the English language (and probably others, too) is horribly bad for communication about probability, allowing such sorts of forms of sophistry to flourish. And the real world is often insufficient to punish educated middle-class people for rounding or flooring the probabilities in the socially desirable direction, even though people making such abuses of probability would get destroyed in many practical endeavours (e.g. betting).
One method for avoiding bias is to identify when one is tempted to engage in such rounding and flooring of probabilities.