Gender and sex is often deliberately conflated by those campaigning for trans rights, on topics such as using the bathroom of the other sex, or competing in sports against those of the other sex, so why is it so bad for Shapiro to conflate the two in his response? As far as his comments go on the subject he clearly states he feels bad for the sufferers and he does not care what people choose to wear, which medical procedures they choose to go through or what they choose to call themselves, so long as he isn't legally compelled to respond in a certain way.
As for the question of whether it's a mental illness, of course it is. Bringing homosexuality into the equation to refute that makes no sense. In this day and age, unless you or your parents are very religious, being gay has little to no adverse impact on your self esteem or quality of life. In the west it would seem to correlate to a better quality of life, at least for men. The same obviously cannot be said for gender dysphoria, which has a similar impact on suicide attempt rates as severe clinical depression.
If someone has depression, you say they have depression. If someone is bipolar, you say they are bipolar. Mislabelling gender dysphoria as some kind of new age fad does nothing to help the sufferers.