Is there a correlation between mental disorders and mental rigidity?
I suspect that when people have very strong beliefs and it happens that this beliefs are dysfunctional they can incur into mental disorders. To further clarify the question it can be also reformulated in another way. Is it possible to state that most of people change their beliefs to become adaptive to the requirements of society while stubborn people don't?
Is that correct?
Philip gave a pretty good answer (+1). There's also a phenomenon called "belief perseverance", typically defined as
maintaining a belief despite new information that firmly contradicts it
This IMHO is a little closer to "mental rigidity"; jumping to conclusions is sometimes done because one is biased toward his "rigid" (prior) idea, i.e. a form of confirmation bias, although certainly other forms of cognitive deficits can lead to incorrect inferences.
The two-factor [theoretical] approach to delusions basically includes belief perseverance, at least in an extreme pathological form:
Central to the two-factor approach is that the presence of any delusion, regardless of theme or medical context, must be accounted for by answering two distinct questions: 1) how did the unusual thought content first arise?; and 2) having once entertained the idea, why does the patient fail to reject it?
Thus the question of whether "mental rigidity" causes other "psychological problems" is a bit circular because (in extreme forms) perseverance in unusual beliefs is one of the symptoms of mental disorders that include delusions (schizophrenia, psychotic depression etc.), which are defined operationally, so in terms of symptoms. And we're getting a bit further afield here, but I do think it's worth mentioning that some of the debate of whether delusions are socially constructed hinges on what beliefs are sufficiently unusual in a given society:
it can be extremely difficult to develop an operational way of determining what is or is not a part of normal experience, and it is correspondingly difficult to distinguish clearly between a belief that is truly delusional and one that is merely unusual, arcane or irrational
Some psychiatrists have even investigated the perseverance in common (but non-factual) beliefs like racism from a delusional-phenomenon perspective. Religious beliefs are also commonly brought into discussion:
In clinical practice, no clear guidelines exist to distinguish between "normal" religious beliefs and "pathological" religious delusions. Historically, psychiatrists such as Freud have suggested that all religious beliefs are delusional, while the current DSM-IV definition of delusion exempts religious doctrine from pathology altogether. From an individual standpoint, a dimensional approach to delusional thinking (emphasizing conviction, preoccupation, and extension rather than content) may be useful in examining what is and is not pathological. When beliefs are shared by others, the idiosyncratic can become normalized. Therefore, recognition of social dynamics and the possibility of entire delusional subcultures is necessary in the assessment of group beliefs. Religious beliefs and delusions alike can arise from neurologic lesions and anomalous experiences, suggesting that at least some religious beliefs can be pathological.
And even further out, some famous atheists have argued that some religious beliefs can make a society as a whole more dysfunctional.
Now if you actually want to define stubbornness as not adapting one's beliefs to those of those around him (like in your second-to-last sentence/question)...
Is it possible to state that most of people change their beliefs to become adaptive to the requirements of society while stubborn people don't?
... the more common term for [the opposite of] that is (social) conformity:
the act of matching attitudes, beliefs, and behaviors to group norms
But do note that conformity may include machiavellianism etc., so not really changing one's inner beliefs, but pretending to do so for the purpose of fitting better in society.
Even glossing over that, some nonconformists (e.g. schizophrenics) may exhibit belief perseverance, but other non-conformists may exhibit huge cognitive flexibility, much more so than most people around them. In particular, think of those non-conformists that pioneered new fields of science, etc. So I think the final part of your question is conflating "mental rigidity"/stubbornness with non-conformism, but the two are not really the same concept, although overlap/intersection is certainly possible in some individuals.
I've read that a tendency to "jump to conclusions" has an impact on certain psychological afflictions, such as having delusions. As you may know, the definition of a delusion is as follows (this is just from Google dictionary):
an idiosyncratic belief or impression that is firmly maintained despite being contradicted by what is generally accepted as reality or rational argument, typically a symptom of mental disorder.
I am assuming that that sort of uncritical thinking is at least part of what you meant by "mental rigidity."
