Do I Care?

The title sounds a lot like a rhetorical question from some popular rock song, but in my case, it is a genuine question I am asking myself. As to why, is not totally clear to me too, but hopefully as the article progresses, we can get some sort of a rough idea at least.
First, let me complete the question - this is not a 'do I care about the world' kind of question. The question in its totality is 'Do I care what others think or feel about me?'
Had I been confronted with this question a few years ago, my answer would have been an outright no. However, as of late, I am unsure of what the answer should be. The thing is, people are always making opinions about you. Most of these opinions are based on how they observe you at a point in time. Sadly, therefore, these opinions are based on assumptions and incomplete information. Moreover, these opinions affect how those people interact with you and value you. Now the answer may seem that - well those who matter - will end up making an opinion about you over a period of time which will be a fair one, while the others don't matter anyway, so why bother? However, this solution weakens, when potentially significant people have to chose whether to interact with you or not. Often, to make this choice people don't have too much time to expend, all they have is their opinion of you in a short period of interaction. Also, in the beginning, people are more averse to accepting your idiosyncrasies than when they know you well. So the question now boils down to whether it is worth living your life trying to make an extra effort in portraying yourself to be something you are not, in an effort to capture potential opportunities or living freely, as you are, perhaps letting go of potentially enriching opportunities at the cost of personal freedom?
I find this a tough choice to make, because I value both equally highly... this is where my quandary lies... I hope to find the answer... but don't really know whether one is possible without making a sacrifice..., which sacrifice to make is a tough choice too...