A personal interpretation of a quote as part of the quote is not appropriate in my opinion.

Additionally, the quote is not saying not to care. I would interpret this quote as saying you should be who are, do what you feel, say, etc without fear. In no way does an affirmation of being oneself dismiss regard for others' feelings. I can bravely be "my truest self" while still being considerate of others. Saying "it's your life, not theirs" is a colossal display of either ignorance or inhumanity.

Finally, this is a quote by Bernard M. Baruch...

ummm....that's not what the quote is about at all...it's not about simply living your life as you choose because it's your life....