If I was as easily offended as you are I could pick up on your comment about things being "just" mental illness and how that could imply that these problems are not serious. However, I shall not pursue this path because I do not want to make things any worse than they already are.
Genital dysphoria and being transgender are not exactly the same thing. Transgender means changing gender identity, not necessarily the same as biological sex. Genital dysphoria is the condition of having genitals which do not match the person's sexual identity, and this may or may not be resolved by becoming transgender. Since dwarves do not have much of a concept of gender, I could more easily imagine them having genital dysphoria than changing gender identity, since this would have little effect on them.
one does not "become transgender" being transgender is having genitals that do not match your gender identity. Your gender identity is in fact your biological gender. You are biologically female if you are a transgender female, you just have male genitalia. You are, no offense, not speaking from a position of experience. You just now realized that this is not a psychological illness. I'm not saying I am the last word in gender identity, but I have spent some time on this to be more aware and empathetic. What I'm telling you is what I have learned from transgender individuals. Who are, generally, the ones you want to go to about this issue.
I assume you are under the impression that transgender involves surgery or hormone therapy, but that is not the case. It it simply a matter of your gender not matching your genitalia, although that could also be intersex, but that's an entirely different issue. (ambiguous or both genitalia being intersex.)
This is not an "easily offended" thing. Really, if you are using words or engaging in behavior that hurts someone, you should want to not do that. Ethical hedonism and all that.
BTW, please don't lecture me on psychological illness, I am on disability after a suicide attempt many years ago, I have schizo-effective bipolar disorder (that's bipolar with traits of schizophrenia.) While I sometimes use the term mental illness, psychological illness is a better term because it does not give the impression it is all in the person's head, made up and what have you. I realize sharing this exposes a weakness on my part, and it often leads to trouble for me, but I will just do it anyway, and hope I don't come to regret it.