Being lgbt isn’t a mental illness. Not medically speaking, anyway. Maybe they were considered such in the past. Go far enough back and we used bloodletting as a common treatment, our understanding generally improves with time. I have no desire to go back to an era where lgbt people were persecuted.
With respect to your other point. “Children” is a broad category. Pre-pubescents are not “changing sex”. Instead we are being encouraged to respect their gender identity, and not reject gender-non conforming behaviors [1]. Teens may take puberty blockers to buy time, this also isn’t “changing sex”. Perhaps HRT is what you mean by changing sex, and yes some teenagers are able to access the HRT of their preferred gender. The science on this is pretty clear, that suicide rates of trans people is drastically lowered when in a gender-supportive environment, and their mental well-being is infinitely better.
[1] I implore you to watch this video: https://youtu.be/h60YLGDJ6n0
Edit: despite what a child comment I cannot reply to is saying, while over-medicalization and misdiagnosis is definitely something to watch out for (being gender-nonconforming is not the same as being trans and this is why education about lgbt issues is important), the vast majority of transgender youth do not suffer from an overabundance of societal and medical acceptance for their issues.
Puberty blockers are indeed not a drug to prescribe lightly. Same with SRS, it should not be handed out like candy. People who have only had gender dysphoria for a short time may indeed be better served by a “wait and see” approach. All of these things I can agree with.
If you are under the impression that being trans isn’t stigmatized enough and all the kids might turn trans if we aren’t careful, I’m simply going to disagree with you. There’s no evidence of this.