Being transgender isn't considered a mental illness

Transgendered people commit suicide at alarmingly higher levels than non-transgender people. Source

More than half of transgender male teens who participated in the survey reported attempting suicide in their lifetime, while 29.9 percent of transgender female teens said they attempted suicide. Among non-binary youth, 41.8 percent of respondents stated that they had attempted suicide at some point in their lives.

Even if you claim that "it's because they're being ridiculed", they will be surrounded by men who will look down upon them as freaks, and other people who traditionally lean right who certainly will not change their ways.

You want these people to serve in combat roles where having a sound state of mind is required, and you want to put people who have gender dysphoria among other possible aliments up there against an enemy. No thanks, not for national security would I ever consider anything that could give my side a disadvantage over an enemy.