I think a good way to separate what the field of psychiatry should be trying to treat is to look at some disorders in detail. Let's examine the difference between obsessive compulsive disorder and obsessive compulsive personality.
The obsessions and compulsions a person with obsessive compulsive disorder experiences are ego dystonic. This means the person with ocd may feel compelled to touch something three times in order to stave off disaster but is aware that the compulsion is irrational. They may wash their relatively clean hands a dozen times to get rid of contamination but know they've washed their hands enough after one washing. To the person with the disorder the need to carry out the compulsion is burdensome but the inability to carry it out can in the short term causes severe distress. This is not a mental illness simply because touching things a magical number of times is culturally abnormal but because of the impairment and distress it causes to the person suffering from it. The person with ocd also has great insight into the lack of logical nexus between their compulsions and their goals.
Compare this to someone who has an obsessive compulsive personality or who is otherwise described as "perfectionistic". They may sleep with a room temperature of 68 degrees because they think it's the perfect temperature for good sleep. They may drink one and a half cups of coffee because they think it's the perfect amount. But they aren't compelled to do anything burdensome just to assuage feelings of anxiety and inner tension. If they have to sleep at 67 degrees it may not be optimal but it's far better than 74. They may be different from the norm and others may find them particular or difficult but they would not have an illness whereas the first person does.
It is a relevant consideration for psychologists to ask themselves whether they are enforcing cultural norms or treating maladaptive, distressing psychological conditions. I have no doubt that psychology done poorly carries forward cultural judgments, but most mental illness involves thinking and behavior that is different from what is typical by type rather than degree and experienced as painful to the person with the condition.