Generally speaking, mental illness alone cannot synthesize a political view that doesn't already exist. Normal mentally ill people will tend to have views that are based on their environment - so if they're raised religious, then they believe they are able to talk to angels. If they're in a conspiracy community, they believe the CIA is beaming thoughts into their head, etc.

These are all based on existing normal political thoughts. But the only exception is that they are unable to distinguish imagination from reality, so they project those views into concrete perceptions of what's going on around them.

When you see someone pop up with some strange political perspective that you've never heard of before in your life, you can safely bet that this person comes from a community that you are unaware of. In the case of these trans shooters, it's most likely CIA groomers on Discord.