Treating it as a mental illness only has bad consequences if the society has a very negative view of mental illness. As for problems only being caused by non acceptance, that is also an assumption - the genital dysphoria itself can be very distressing for some, seeing the wrong body all the time, regardless of anyone else's opinions.
The discussing this was replying to was about
one of us labeling transgender as a mental illness, in this actual discussion. What hypothetical dwarven society would think of it is not the same issue that was being dicussed.
In our society, labelling some behavior you disagree with as a mental illness does in fact carry very negative connotation that's it's not "proper thinking", and that it's an illness which should be "cured" so they "think right". Until recent decades homosexuality was labeled the same.
"Don't label transgender people as mentally ill in this thread" => "Yes, but what would dwarves think of it?" isn't a valid rebuttal. I do think smeeprokect overreated to the term "sex-dysphoria" a little, but still, bringing in non-existant societies hypothetical views on mental illness isn't a coherent addition to the debate. But even then, I doubt it would be different in any society which even had a concept of metal illness. "metal illness" implies wrong thinking which should be fixed, no matter how nice we are about it.