This statement is almost always bullshit.  When it’s not it’s a sign of *supreme* narcissism.

What kind of a person care what *no one* thinks?  Parse it a different way.  How would you feel if you heard someone say “I don’t care how I make anyone feel.”  Kind of an asshole, no?

So, don’t kid yourself.  The goal is not to stop caring what others think.  The goal is to behave in a way that is kind, avoids hurting others, doesn’t impose on people.  If you can’t say anything nice, and a toddler will not be run over because you didn’t speak up, perhaps you should NOT speak up.  If, conversely, you may save actual harm to others by speaking up you are morally bound to do so.  Think hard about if it’s harm you’re saving others, or just pushing your opinion on them.