Two years ago, many trans people were banned from serving in the US military. The ban was reversed earlier this year, but that's kind of the point: there are ongoing attacks against trans rights that are still happening right now and need attention. So that is why it gets the focus.
As much as I want the government to stay out of bathroom policies, there's no recognized right to use whatever bathroom you want. Nor is there any right to join the military.
I'm not sure what you mean. Recognized by who? If you meant government officials, that's specifically the point: some may not recognize that it is a right, so the goal is to get them to recognize that it is.
Being trans is not a protected class, so discrimination against trans people is legal in many states. On top of that, states keep passing unconstitutional anti-trans bills like NC's famous "bathroom bill," which someone has to fight in court