Well, that depends on a situation. If you're in an environment where people are united by a common goal and assume good faith, then admitting you done goofed up

Well, that depends on a situation. If you're in an environment where people are united by a common goal and assume good faith, then admitting you done goofed up (when you did) is the best way - everybody knows you realized your mistake and will try to do better, and people can move on - and usually will be glad to offer you to help fixing it. And they'd know they can count on you to own up to your mistakes - so they'd be ready to listen if you say something isn't a mistake. If you are in a "cancel culture" situation, then people that surround you are not you friends, and they do not have common goals with you. You can not win. Best thing is to get out of that situation ASAP, if you can not - minimize your losses in any way you can. And continue looking to get out of this situation, because you can not win, and you will surely lose sooner or later. Try to still be kind to others - you won't fix the broken culture, but at least you can have a little island of non-awfulness around you.