From the costs of rationality wiki:

Becoming more epistemically rational can only guarantee one thing: what you believe will include more of the truth . Knowing that truth might help you achieve your goals , or cause you to become a pariah. Be sure that you really want to know the truth before you commit to finding it; otherwise, you may flinch from it.

The reason that truth seeking is often seen as being integral to rationality is that in order to make optimal decisions you must first be able to make accurate predictions. Delusions, or false beliefs, are self-imposed barriers to accurate prediction. They are surprise inducers. It is because of this that the rational path is often to break delusions, but you should remember that doing so is a slow and hard process that is rife with potential problems.

Below I have listed three scenarios in which a person could benefit from considering the costs of truth seeking. The first scenario is when seeking a more accurate measurement is computationally expensive and not really required. The second scenario is when you know that the truth will be emotionally distressing to another person and that this person is not in an optimal state to handle this truth. The third scenario is when you are trying to change the beliefs of others. It is often beneficial if you can understand the costs involved for them to change their beliefs as well as their perspective. This allows you to become better able to actually change their beliefs rather than to just win an argument.

Scenario 1: computationally expensive truth

We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil. Yet we should not pass up our opportunities in that critical 3%. – Donald Knuth

If optimization requires significant effort and only results in minimal gains in utility, then it is not worth it. If you only need to be 90% sure that something is true and you are currently 98% sure that it is, then it is not worth spending some extra effort to get to 99% certainty. For example, if you are testing ballistics on Earth then it may be appropriate to use Newtons laws even though they are known to be inexact in some extreme conditions. Now, this does not mean that optimization should never be done. Sometimes that extra 1% certainty is actually extremely important. What it does mean is that you should be spending your resources wisely. The beliefs that you do make should lead to increased abilities to anticipate accurately. You should also remember occams Razor. If you are committing yourself to a decision procedure that is accurate, but slow and wasteful then you will probably be outcompeted by others who spend their resources on more suitable and worthy activities.

Scenario 2: emotionally distressing truth

Assume for a moment that you have a child and that you have just finished watching that child fail horribly at a school performance. If your child then asks you, while crying, how the performance was. Do you tell them the truth in full or not? Most people would choose not to and would instead attempt to calm and comfort the child. To do otherwise is not seen as rational, but is instead seen as situationally unaware, rude and impolite. Obviously, some ways of telling the truth are worse than others. But, overall telling the full truth is probably not going to be the most prudent thing to do in this situation. This is because the child is not in an emotional state that will allow them to handle the truth well. The truth in this situation is unlikely to lead to improvement and will instead lead to further stress and trauma which will often cause future performance anxiety, premature optimization and other issues. For these reasons, I think that the truth should not be expressed in this situation. This does not mean that I think the rational person should forget about what has happened. They should instead remember it so that they can bring it up when the child is in an emotional state that would allow them to be better able to implement any advice that is given. For example, when practicing in a safe environment.

I want to point out that avoiding the truth is not what I am advocating. I am instead saying that we should be strategic about telling potentially face-threatening or emotionally distressing truths. I do believe that repression and avoidance of issues that have a persistent nature most often tends to lead to exacerbation or resignation of those issues. Hiding from the truth rarely improves the situation. Consider the child if you don't ever mention the performance because you don't want to cause the child pain then they are still probably going to get picked on at school. Knowing this, we can say that the best thing to do is to bring up the truth and frame it in a particular situation where the child can find it useful and come to be able to better handle it.

Scenario 3: psychologically exhausting truth

If we remember that truth seeking involves costs, then we are more likely to be aware of how we can reduce this cost when we are trying to change the beliefs of others. If you are trying to convince someone and they do not agree with you, this may not be because your arguments are weak or that the other person is stupid. It may just be that there is a significant cost involved for them to either understand your argument or to update their beliefs. If you want to convince someone and also avoid the illusion of transparency, then it is best to take into account the following:

• You should try to end arguments well and to avoid vitriol - the emotional contagion heuristic leads people to avoid contact with people or objects viewed as "contaminated" by previous contact with someone or something viewed as bad—or, less often, to seek contact with objects that have been in contact with people or things considered good. If someone gets emotional when you are in an argument, then you are going to be less likely to change their minds about that topic in the future. It is also a good idea to consider the peak-end rule which basically means that you should try to end your arguments well.
• If you find that someone is already closed off due to emotional contagion, then you should try a surprising strategy so that your arguments aren't stereotyped and avoided. As elizer said here: 

• The first rule of persuading a negatively disposed audience - rationally or otherwise - is not to say the things they expect you to say. The expected just gets filtered out, or treated as confirmation of pre-existing beliefs regardless of its content.

• Processing fluency - is the ease with which information is processed. You should ask yourself if your argument worded in such a way that it is fluent and easy to understand?
• Cognitive dissonance - is a measure of how much your argument conflicts with the other persons pre-existing beliefs? Perhaps, you need to convince them of a few other points first before your argument will work. People will try to avoid cognitive dissonance. Therefore, it is better to start off with shared arguments and in general to minimise disagreements. It is often the sounder strategy to modify and extend pre-existing beliefs.
• Inferential distance - is about how much background information that they need access to in order for them to understand your argument?
• Leave a line of retreat - think about whether they can admit that they were wrong without also looking stupid or foolish? In winning arguments there are generally two ways that you can go about it. The first is to totally demolish the other persons position. The second is to actually change their minds. The first leaves them feeling wrong, stupid and foolish which is often going to make them start rationalizing. The second just makes them feel wrong. You win arguments the second way by seeming to be reasonable and non face threatening. A good way to do this is through empathy and understanding the argument from the other persons position. It is important to see things as others would see them because we don't see the world as it is; we see the world as we are. The other person is not stupid or lying they might just in the middle of what I call an 'epistemic contamination cascade' (perhaps there is already a better name for this). It is when false beliefs lead to filters, framing effects and other false beliefs. Another potential benefit from viewing the argument from the other persons perspective is that it is possible that you may come to realise that your own is not as steadfast as you once believed.
• Maximise the cost of holding a false belief - ask yourself if there are any costs to them if they continue to hold a belief that you believe is false? One way to cause some cost is to convince their friends and associates of your position. The extra social pressure may help in getting them to change their minds.
• Give it time and get them inspecting their maps rather than information that has been filtered through their map. It is possible that there are filtering and framing effects which mean that your arguments are being distorted by the other person? Consider a depressed person: you can argue with them, but this is not likely to be overly helpful. THis is because it is likely that while arguing you will need to contradict them and this will probably lead to them blocking out what you are saying. I think that in these kinds of situations what you really need to do is to get them to inspect their own maps. This can be done by asking "what" or "how does that make you" type of questions. For example,“What are you feeling?”,“What’s going on?” and“What can I do to help?”. There are two main benefits to these types of questions over arguments. The first is that it gets them inspecting their maps and the second is that it is much harder for them to block out the responses since they are the ones providing them. This is a related quote from Sarah Silverman's book:

• My stepfather, John O'Hara, was the goodest man there was. He was not a man of many words, but of carefully chosen ones. He was the one parent who didn't try to fix me. One night I sat on his lap in his chair by the woodstove, sobbing. He just held me quietly and then asked only, 'What does it feel like?' It was the first time I was prompted to articulate it. I thought about it, then said, "I feel homesick." That still feels like the most accurate description--I felt homesick, but I was home. - Sarah Silverman

• Remember the other-optimizing bias and that perspectival types of issues need to be resolved by the individual facing them. If you have a goal to change another persons minds, then it often pays dividends to not only understand why they are wrong, but also why they think they are right or at least unaware that they are wrong. This kind of understanding can only come from empathy. Sometimes it is impossible to truly understand what another person is going through, but you should always try, without condoning or condemning, to see things as they are from the other persons perspective. Remember that hatred blinds and so does love. You should always be curious and seek to understand things as they are, not as you wish them, fear them or desire them to be. It is only when you can do this that you can truly understand the costs involved for someone else to change their minds.

If you take the point of view that changing beliefs is costly. Then you are less likely to be surprised when others don't want to change their beliefs. You are also more likely to think about how you can make the process of changing their beliefs easier for them.

Some other examples of when seeking the truth is not necessarily valuable are:

• Fiction writing and the cinematic experience
• When the pragmatic meaning does not need truth, but the semantic meaning does. An example is "Hi. How are you?" and other similar greetings which are peculiar because they look the same as questions or adjacency pairs, but function slightly differently. They are like a kind of ritualised question in which the answer is normally pre-specified or at least the detail of the answer is. If someone asks: "How are you" it is seen as aberrant to answer the question in full detail with the truth rather than simply with fine, which may be a lie. If they actually do want to know how you are, then they will probably ask a follow up question after the greeting like "so, is everything good with the kids".
• Evolutionary biases which cause delusions, but may help in perspectival and self confidence issues. For example, the sexual over perception bias from men. From a truth-maximization perspective young men who assume that all women want them are showing severe social-cognitive inaccuracies, judgment biases, and probably narcissistic personality disorder. However, from an evolutionary perspective, the same young men are behaving more optimally. That is, the bias is an adaptive bias one which has consistently maximized the reproductive success of their male ancestors. Other examples are the women's underestimation of men's commitment bias and positively biased perceptions of partners

tldr: this post posits that truth seeking should be viewed as an optimization process. This means that it may not always be worth it.