'SEAL training was the great equalizer. Nothing mattered but your will to succeed. Not your color, ethnic background, education, or social status.'
-Admiral William H. McRaven
In combat soldiers don't care about the sexual orientation or gender of the person guarding their back. They only care if they can do their job. In times of stress it's easier to form bonds with the people you experienced it with, especially when those people helped safeguard your life. That makes it harder for veterans to dislike trans people as much because they served with a trans person. In America we have (or at least pretend to have) a huge fetish for veterans, and it's harder to attack a trans veteran. People will probably be a bit more willing to listen to a cis veteran said 'I served with those people, they're alright'.
It's also bad optics. Each hot button trans issue is a battleground for trans rights. Losing one and not caring because I don't want to join the military is a mistake. It's like a tug of war, where the more protections and rights trans people have the more the rope is pulled to our side, and vice versa. The more ground we gain, the longer it takes for others to take it away from us. The ban reminds us our rights could be taken from us on the whim of the government.
Visibility of trans people in culture is important for acceptance. It's harder to think I'm an abomination, pedophile, or fetishist if you actually meet me. When you actually get to know me you realize I'm actually in many ways like most people. We're all actually not that different from one another. Don't let cynical politicians divide Americans against each other to exploit you for political gain. Trans people often value love, family, commitment, integrity just like cis people. For our transgender troops, they also value protection of democracy, freedom, discipline, and protecting the country. With proper visibility people gradually realize their mental image of how trans people are all like is built on stereotypes and that there exist trans people of all sizes, colors, and personalities. They'll stop thinking trans people are merely caricatures of their gender.
Separate but equal might be a familiar phrase if you understand American history. The courts eventually understood that was a fantasy. If the oppressed minority had equal rights and opportunities then almost by definition it means a lack of separation, because why would such separation be necessary? Like the tug of war for mindshare and rights, losing this battle is a loss for trans rights and acceptance. I don't want to tell a kid that when they grow up they can be anything they want. ...Except for the president or a military service member because people hate us. That kid probably gets shit all the time from kids to disapproving family members, so they probably have very low self esteem. They might worry they will never pass or they might start to hate themselves. The despair may be so deep, they consider self harm and threaten to tear apart the lives of not only themselves but their family and friends as well. One day they see trans people in the military being honored and valued. Perhaps I'm not so worthless after all. If they can do it, maybe I can too. Visibility gives voices to those who are silenced and visibility to the invisible.
In reality when a group gets less rights than another group, the government sanctioned discrimination leads to more discrimination from ordinary citizens towards the group. That effect is insidious and affects all trans people, not only those who wish the serve.
We can't on one hand argue bothering to give trans people rights is pointless because they are so rare and on the other hand complain they are so common in the military, they will cost too much in healthcare. If we really cared about saving money, don't do senseless regime change wars that cost trillions of dollars. The cost of Viagra the military spends far outweighs trans healthcare. It's not a big deal in the grand scheme of things. Isn't is suspicious nobody is talking about changing healthcare benefits for trans individuals if budget was actually a concern?
If we really cared about logistics for hormone replacement therapy, then it is suspicious nobody is suggesting only banning trans men from the military due to the vials of testosterone they have to take. Trans women can take high-dosage pills, of which many can fit in a small pill bottle. We don't hear anything about the realities of logistics or the medications trans women vs trans men take because it's not about that.
It's not about logistics. It's not about cost. It wasn't about water fountains in the 60s and it's not about bathrooms or logistics today. Trans people are an oppressed minority and as such the small inconvenience of having trans people serve alongside their cis brother and sisters is outweighed by the benefits of inclusion. Critics might claim the ban only really affects those diagnosed with gender dysphoria medically. Many trans people know this means very little, because that diagnosis is used to obtain hormone replacement therapy in the first place. Many people diagnosed with gender dysphoria don't actually have gender dysphoria in the clinical sense (checklist of symptoms including having trouble functioning in society) but rather dysphoria in the colloquial sense (any level of discomfort with their gender and body which often is not crippling). We're not sending useless tokens of social justice into battle, and that's why a trans service member made it to the Navy SEALs.
Perhaps you are wary of transgender troops out of purely logistical or financial reasons even though most people who claim such are actually uneasy with trans people and looking for a reason to shut them down. Maybe you don't have such unconscious biases. But realize that most people do, and the transgender ban is being pushed by bigots who would take our rights away one step at a time if they could. Is this the company you want to keep, and the policies you want to support? Aren't you worried the government will do more to harm trans people and you just aided them on their quest?
As the New Yorker said, aspiring tyrants like Trump exert control over the people because they can. It is abhorrent for Trump to take away the rights of soldiers who would die to protect him. Patriotism is shown through actions not worship of symbols. Our trans service members demonstrate patriotism in spades. If we care about supporting the troops, then support all of the troops. It's time for freedom-loving Republicans to show us just how much they care about justice and liberty for all. Our cause is just. You can still choose to be on the right side of history and choose love, not hate. Lord knows we already have too much of the latter.