It's always white males who are stuffed full of white privilege who demand that everyone stop being so sensitive. I suspect it's because racism, sexism, and the dislike of anything that isn't 'the norm' (US/European centric white maleness), is so ingrained and accepted in our society that many of us just don't see it or simply don't care.
And I speak as a white male who is the beneficiary of centuries of white privilege. But even though I unquestionably benefited from it, that doesn't mean I want others to conform to what I want. I can see a lot of racism and sexism, and I can do things to not be a part of it. Telling people to 'buck up' and to 'stop being so sensitive' is exactly like Joan Rivers shrieking a horrible fat joke at some over wight person and then telling them to grow up or shut up and lose some weight if they don't like it.
As a matter of fact, people DO NOT need to stop being so sensitive, white males need to realize they don't run everything any more and they need stop being raging assholes.
