I understand this viewpoint but I feel it does more harm than good. It just teaches sexist people and racist people what NOT to do. Doesn't change their views or beliefs. It instead makes THEM feel like the victims.
But if the goal is to shame them or expose them then yes this is the right course. I just don't think its helpful to the overall goal of people getting along. Just divides people more.
Maybe "people getting along" is not the only goal here. If you keep insulting the people around you, they're going to ask you to stop; if you didn't realize you were doing it, the best thing to do is to recognize that and
stop. It isn't to say "oh, why can't we all just get along?"
When you're called out, it's not hard to just say "oops, I fucked up, sorry" and move on. Everyone screws up sometimes; everyone has some dumb opinions or makes some stupid mistakes. Especially in the 21st century - when your words are potentially being viewed by a lot more people, and you can end up exposed to a lot more opinions that previously wouldn't have been able to find a voice - it's easy to put your foot in your mouth without realizing it, or to have people point out problems you wouldn't have seen on your own. It doesn't make you a terrible person.
When it starts to out people as awful is when they insist on making it all about themselves - suddenly this is a deep and serious challenge to them; clearly this is all about their guilt or innocence in some vast cosmic trial that they must defend to the death
For example, I've read a bunch of people who agree what was said was "asshole-ish" but also say its not "Much-of-a-big-deal". And now other posters are attacking THEM for that view.
Maybe your insistence on interpreting it as an "attack" is part of the problem. If you acknowledge you screwed up (and yeah, anyone who tries to argue this isn't a big deal has screwed up), then you should maybe just... try and listen to what people are saying? Apologize, and avoid making that mistake in the future?
Just... let the chip fall off your shoulder, now and then. It isn't necessary to "defend' yourself every single time. Sometimes you can just accept it as a chance to learn the impact your words are having on other people, and adjust them to suit. (And if you don't care how your words are being taken by other people - why are you talking in the first place? Reaching other people is what words are
for.)