Specifically regarding Trans and Questioning and all the other ones relating to gender dysphoria I don't think it's discriminatory that they can't serve. Just like diagnosed bi-polar or the like can't. It's not in anyone's good. I understand why people argue that varied sexual orientation is a normal thing. Normalizing gender dysphoria is beyond me.
Regardless of whether it’s fair or not, you can’t call being treated equally a ‘special privilege’
I was somewhat picking on your wording, but making a point. They absolutely can serve openly. They cannot serve while openly exhibiting some behaviors. There is no inherent privilege of exhibiting any behavior at all in the military. There are many behaviors one may need to hide while in the military.
So let’s phrase it differently. For LGBTs in the military to be able to have a public love life is equality, not ‘special privilege’.
The vast majority of LGBT rights aren’t giving them anything special