The people in charge in the U.S. want to eliminate transgender people so that they can have men and women in neat, separate boxes and continue to oppress women as they have been for centuries.
I personally think it's more about manufacturing an 'other' to blame everything on and unite people in hate.
There's little benefit to targeting women for oppression in the modern economy - they're just more undifferentiated labour to be exploited (though it remains possible to pay them less). I think this was meaningfully different when living off a single income was a realistic proposition.
There's no single unified group of "people in charge in the U.S.". There are various people with varying amounts of power. Some of them are religious nutters who interpret their religion as saying that anything other than traditional gender roles is satanic. Some of them are opportunists who see religious nutters as useful idiots, they rile them up over transgender issues in order to get their support for other things (i.e. tax cuts / loopholes for special interests, etc.). Some of them are somewhat liberal, but are still uncomfortable with transgender people and see their political opponents using transgender issues to rile up their base while they do really destructive things (tax cuts / loopholes for special interests, etc.), so they focus their efforts not on defending transgender people, but in trying to attack what they see as the real issues. A small minority of "people in charge in the U.S." are transgender, or very concerned with transgender issues, and are doing everything they can to fight for transgender rights.
Don't forget that the majority of the "people in charge in the U.S." are over 60 years old, and so even basic gay rights are a major departure from the world they were raised in.
And the people who think there are "people in charge" other than a government are deluded fools. Yes, rich people lobby and get special loopholes and exemptions from laws. But, they're hardly a cartel that agrees about things, makes decisions collectively and then implements those decisions by simply passing laws or whatever. Rich people have more influence, but they're not in charge, and they're certainly not working together. If you know anything about the ultra-rich, it's that they're sociopaths. People like that don't work together, they backstab each-other, have vendettas against each-other, etc. They're not "in charge", they're just the loudest voices in the room.