So your claim is that men that want to be women are pedophiles because they want to use the womens restroom?
Who told you they suffer from a mental illness because they are transgender?
You know your questions are really hard to sift out because of the self-diagnosis factor. What's "transgender"? I'm only aware of men and women. BTW, I now identify as the owner of your house. I wasn't born you, but I've always felt like you trapped in this strange body. So I'll be taking over the deed to your property and you have two weeks to be out.
If you disagree and call me by any other pronoun than your first and last legal name, social security number etc., I'm going to sue you for bigotry. If we lived in New York, your failure to identify me by my self-diagnosis would also result in a fine.
Think that sounds absurd? It is no more or less absurd than staring between your legs, seeing a penis and testicles and declaring to the world "I'm not a man, I'm a woman".
Once the barn door has been kicked open for delusions-as-reality where others have to play along, you don't get to pick and choose your favorites. That's not how equality works.