Is it a mental illness?

My friend thinks being trans is a mental illness

If it's treatable with drugs, it's a medical issue.

Many medical issues have psychological side effects as symptoms. The word for that is somatopsychic (physical ailments causing mental or emotional symptoms) as opposed to psychosomatic (imagining physical symptoms or making yourself sick by psyching yourself out).

They used to classify homosexuality as a mental health issue because homophobia.

No, it's not someone "being crazy" just because you think it's weird or unimaginable or the idea makes you uncomfortable.