The thing is, racism and sexism and homophobia still exist. That there is the problem. They all exist in this horrible covert grey area where every place they crop up, it can be argued someone is either too sensitive, or it never happened. People don't get jobs or apartments and other than the boss/owner looking at you kind of suspiciously, you won't know why. Or less overt, people saying 'fag' as an insult and then turning around and pretending they don't think there is anything wrong with being gay. Or people immediately thinking of lazy guys in sombrero's with donkeys when asked to think of a Mexican.
As long as these things exist in real life, one can never know if someones is being funny and making a point, or if they are just bigot and either don't realize or don't care. As someone who has to occasionally deal with homophobia and sexism, I can understand how someone might be reminded of such things and have negative feelings. Imagine you go to a party expecting to have a good time and you are instead greeted by someone who is dressed in a costume of the worst stereotype of your race you can think of. It can't be fun and the person wearing it is now being questioned as to their motives. Is someone who thinks this is funny really someone I want to be friends with? Regardless of their motives, that is telling.
If you are okay with bigotry and inequality in the smallest form, then where do you draw the line, when exactly does what you do/say become racist and not just 'a joke'? Is it when you mean it? Because the people you are directing it at have no idea whether you mean it or not. So you are essentially saying, "Some people might misinterpret this and get upset, but I don't really care if I upset anyone because my fun is way more important and I am either incapable of having fun unless it's at someone else's expense or I am too lazy/not creative enough to think of an actual funny thing to do/say that doesn't have the potential to hurt anyone's feelings." The you expect people not to call you a bigot afterwards?
When someone tells you they were hurt by something you did/said, and your response is:
"Fuck you, it was a joke." or "I can say what I want, you are just censoring me." or "There isn't problem.", then you are an asshole. You are supposed to care how you affect other people in the world. You are supposed to not be a selfish jackass. Sure you have the right to be one, but don't get pissed when people call you on it.
Your response when someone tells you that you have hurt them is supposed to be something like: "I'm sorry, I will try not to do it in the future." followed by an attempt to actually learn what you did wrong so you actually can not do it again.