Of course it's okay. It's a bathroom, not a place to compare genitals. For the thousands of times I've been in the women's bathroom I have not once seen what's going on in anyone else's stall and unless someone was intentionally looking in other stalls I imagine that's the case for literally every other woman who has used public bathrooms as well. I imagine any transgender man who is using the men's bathroom but has not undergone full surgery would be using the stall in there too, so again, same logic applies.
I don't mind my daughter sharing a bathroom with trans people, it doesn't make any difference as far as I'm concerned unless she's peeping in stalls, in which case she is the problem and not the trans person. The idea that she's somehow at risk because trans people are inherently dangerous or predators is ridiculous and there's nothing to back it up other than people's widespread misunderstanding.
As for the military, they should be allowed in as long as they are capable of doing the job. The standards should be the same as for anyone else. Once upon a time only straight white men were considered qualified and there was a huge resistance to anyone else being allowed in. It doesn't seem that allowing women, other races, and gays into the military has caused it to self-implode yet so I'm not sure why people are still under the impression that these things matter at all.