In case anyone's in any doubt about whether there's any factual basis for this:

Mass shooters are not disproportionately transgender, contrary to claims

This CNN article states it well:

Such a move would represent a dramatic escalation of the Trump administration’s fight against the rights of transgender Americans.

That's it. This is just the fascists finding another way to victimize trans people, because they enjoy doing that and it keeps the morons' attention diverted from real problems.

And this bit is also good in the article (warning: disgusting quotes from Trump admin people):

The goal of the potential ban, according to the Justice official, is “to ensure that mentally ill individuals suffering from gender dysphoria are unable to obtain firearms while they are unstable and unwell.”

Because gender dysphoria is included in the American Psychiatric Association’s Diagnostic and Statistical Manual of Mental Disorders, also called the DSM, it is diagnosed as a mental disorder. (The DSM is the handbook used by health care professionals as the authoritative guide in diagnosing mental disorders.)

But the gender incongruence – having a gender identity that’s not the one assigned at birth – isn’t what makes gender dysphoria a mental disorder. Having clinically significant dysphoria around the incongruence is what makes it a disorder.

That's surprisingly nuanced and well informed for an article on a mainstream news site.