But it is a mental illness by definition

This is false. From the cleveland clinic:

Is being transgender a mental illness? No. Being transgender (or trans, for short) isn't a mental health disorder. If you’re transgender, it means that you have a different gender identity than the one you were assigned at birth. (Gender identity is defined as the personal sense of one’s own gender.) The desire to convey your gender in the way you feel most authentic is a normal aspect of human expression.

Gender dysphoria is a mental illness (it's listed in the DSM-5), and the best treatment we have for it is gender affirmation. But not all trans people have gender dysphoria. From that same page:

Some trans individuals don’t experience mental health issues at all. Others have mental health issues that aren't related to being transgender. But for some, mental health and gender identity are related. Generally, this isn’t due to being transgender, but to the social stigma that often exists.

It sounds to me like you're not intentionally bigoted, and you also don't seem intolerant. But I think you're misinformed on this one, and calling being trans a mental illness could be very hurtful to some. There's a reason the cleveland clinic document literally starts with "Being transgender is not a mental illness", in addition to having a section below that addresses it (which I quoted above).