Being naked is a natural state. Wearing clothes actually sets off the bodies neuro system, and sends it into fits. If it weren't for the religious shame that has been instilled in most people, it would be the "sane" one's getting naked in public. Everyone would be doing it (as it has been so in the past).

The mentally ill do it for the same reason you do it when you want to go to sleep, or take a shower, or get intimate. It's more comfortable, and more natural. The difference is that you or I might not do it in public because of an unnecessary amount of guilt from society. The mentally inhibited are not inhibited about their bodies in the same way everyone else is.

And when we think about that. Isn't it odd that they are the ones considered mentally ill? lol

Some people with brain damage and some with mental illness do not recognize what is socially appropriate.  They also may not recognize the need for protection provided by clothing.  And some may do it for the mere cussedness of rebelling against the restraints of society.  It depends entirely on the individual.  It is a way to make a statement or to protest the way things are.  I would want an evaluaton of the individual before I ventured an opinion.

It is good to keep some perspective. There are many people who get naked in public without being mentally ill. Sports streaking was a fad, college drunk streaking and so on. There is a guiness record for most nude people photgraph that is higher than a small towns population. Our society is inundated with nudity and sex.

Let me say it again--Some people do it for the mere cussedness of rebelling against the contraints of society.  I don't make any judgment on it, but it's not something that appeals to me.

Taking out clothes in public is a result of social disinhibition or personality disorder. In some mental illnesses such as bipolar mania, social disinhibition is a characteristic feature. In addition, people with advanced dementia tend to show social disinhibition.

Elderly people with recent head injuries can have a condition called chronic subdural hematoma (SDH), social disinhibition can be seen in this condition also. Therefore if the social disinhibition is seen within weeks of a previously normal elderly individual, you must send this person to an emergency medical unit (SDH can be treated). 

Additionally people with serious medical disorders can have a condition called delirium. Here also they can show social disinhibition. So best thing is to see, if the individuals behaviour is recent onset or not. If it is recent onset, you need to show it to a doctor.

In addition, some individuals with some abnormal personalities can take off clothes in public. Best thing here is to avoid them without reinforcing their behaviour or to call law enforcement. Most commonly seen in young males. 

In addition, getting naked in public is NOT a common behavior of the mentally ill.  For example, it is estimated that about one in four people in the UK suffer from a mental illness.  I lived in the UK for just over 5 years and did not see nudity in one-quarter of the population.  I currently live in America.  About 1 in 5 Americans suffer from a mental illness.  Not many get naked in public.

Please remember that the mentally ill includes people with major depression, bipolar disorder and obsessive compulsive disorder  -- and not just schizophrenia or dementia.