The first of these arguments is: X is rich — wealth insulates, so you shouldn't feel sorry for X and yeah you can make fun of them even if they're dying of some horrible disease.
The second of these arguments is: X is from a majority — (the oppressors, oppressor class etc) — so X cannot empathize with Y who is from a minority (the oppressed) and yeah you can make fun of them because numbers insulate.
The third of these arguments is: X is from a minority — but it's a worse-treated minority than Y's minority — so whatever you say, Y has it better and you can let X make fun of Y.
The fourth of these arguments is: you have never walked even one yard (or metre) in X's shoes, so how can you possibly understand X's problems?
The fifth of these arguments is: X has a condition that is perfectly normal in the animal kingdom, but is socially ostracized for insufficient reasons, so society should treat X at least like an animal and not make fun of this condition — which is, after all, within the realm of nature.
The sixth of these arguments is: you are MALE, how can you ever empathize with any X when your only claim to X-empathy is that you had a mother?
There are many more such spurious arguments which are actually ad hominem attacks on your ability to understand, empathize, walk a mile in someone else's shoes, or otherwise translocate your psyche. Run from them. But if you must stand and fight, at least point out what they are, and die a martyr in the full knowledge of what you fought.