I’d answer this is all making a mountain out of a molehill.
There are 1,281,900 people in the US military.
Current estimates have people who identify as transgendered in the US at about 0.6% of the population.
If we assume that the military has the same percentage of trans people as the population then about 7,700 people in the military identify as transgendered. How many of them want sex re-assignment surgery? I do not know but we do know not all transgendered people want to surgically transition. As for hormone therapy it is not hugely expensive (something like $1500 over two years) and surgical transition is around $20,000.
I would submit that the military has nowhere near a 0.6% transgendered population. The military is kind of a hostile place for transgendered people and I would not think many would choose it. Some do, certainly, but I’d be surprised if it was the same as the population at-large.
But let’s pretend there are 7,700 trandgendered people in the military and they all want $20,000 sex reassignment surgery. That would come out to about $154 million or about 0.02% of the US military budget (and that assumes you do it all on one year…the reality is some few would come in each year and do it and be nowhere close to that number).
$154 million is less than the cost of two F-35 fighter jets.
But remember, the real number would be nowhere near that (whatever it is). That is the worst case scenario those opposed to this can come up with.
In the end, of all the issues facing the US and its budget and whatnot, this barely registers. I suppose you could argue it on some philosophical grounds if you want as the principle of the thing but even then it is so remote and abstract a thing for Joe Citizen to get worried about I cannot see it is worth the effort to argue about.
For me, if a transgendered person wants to serve the country and part of us paying for that service is helping them get gender reassignment treatments then fine.