The problem with drawing a conclusion with that little information is that we are really projecting an answer to what we imagine those general statements mean to us. We imagine that not caring if other people judge us means we are retaining control of our lives. We imagine that not caring if we are fully made-up for the day before going in public is part of maturing. To some degree, perhaps even in most cases, those would likely be correct conclusions.
It seems, though, that there is a point at which either of those seemingly healthy mental attitudes is actually problematic. It is not mentally healthy to not care what other people think when there are behavioral changes that impose that disconcern unreasonably on others. Likewise, the degree to which people no longer care how made-up they are, and the difference that represents in their behaviors, are better gauges for determining if "not caring" is mentally healthy or unhealthy.
We have all experienced events that we draw upon for future responses. In fact, that is a good definition for experience. If the event is traumatic, we can condition our minds to move past it, but we can never actually erase the experience from our minds. As events feel similar, whether they are similar or not, we will draw from the experiences we associate with that feeling of similarity.
Again, it will be unique to each individual what is drawn from the same event because of different perspectives and previous experiences. When we offer answers to people without understanding how they associate that experience with other experiences they have had, we are only offering them the same shorted circuitry we have built in our minds. That may help encourage someone to act or it may turn them off, but it does not help someone who needs to be understood in order for behaviors to make more sense. Sometimes "hopping back onto the saddle" is not the best option for someone else. It sounds thoughtful, but it is a thoughtless cliche'.
The bottom line is that we all have mental health issues, if we are honest with ourselves. Why and how they manifest may have similarities, but, ultimately, each person has unique experiences from every other person. Many people suppress their mental health issues. They pretend their personal interpretation is the only perspective from which any event can be seen or any situation handled. I imagine people to whom I think that applies; others will apply that image to me. Should others care what I think? Should I care what others think?
Those cannot be answered "yes" or "no." How was the thought intended? How was the thought supported? How was the thought applied to the other person's situation rather than drawn from an experience they imagine is similar? What credentials does the person have who is offering the thought? How much does the person receiving the thought respect the opinion of the person offering it? What authority does the person offering the thought have over the recipient?
Because we factor those questions in based on our perceptions, we care less that some people think we should go to hell than we do that others are slightly disappointed with us. It is also why it stings more when some people tell us to go to hell than it does when other people suggest the same destination.
Obviously, there is no definitive answer to the question of whether or not caring anymore is a mental health issue. Not caring, like any attribute, is one variable factor in an equation that can have negative or positive results. Behavioral changes are better indicators of mental health issues and improvements in mental health. What we care and don't care about are certainly important to our mental health, but, ultimately, the only way to know whether it is an issue or not is to look at the resulting behaviors.
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Some other posts you might enjoy:
Firing My Shrink
Welcome to My Nightmare
My Mom's Computer
Surviving in a Sea of Depression
Inner Struggles