Ah, yes, looking it up now it is confirmed. I figured that to be the case but was waiting for a real reveal, figuring Esmail was going to draw it out and not just give us the direct confirmation by way of the wardrobe.
I don't think it has anything to do with being afraid of outing himself as a cross-dresser. Rather, it's all about ensuring people are not aware of his multiple roles: he's the minister of state security, and he's also a massive organizer/head of a hacking outfit. His crossdressing is presumably the only way he felt comfortable being able to play both roles, because if he was outed as being both, I'm sure he'd be in a world of shit. He couldn't just say, "oh, they are my dresses because I do something else when not acting as a Chinese official."
For the longest time though, I just thought Whiterose was an incredibly ugly woman. But after seeing the wardrobe scene with the minister, I was almost certain he was crossdressing, but couldn't guarantee it. But as BD Wong is credited as Whiterose (never thought to look it up before!), that confirms suspicions.
However, a wiki on the show claims Whiterose is actually transgender, and delineates male and female behavior between his dual roles. I don't know if that has been explicitly confirmed or is just a hunch... he's definitely crossdressing, good enough to make me think it's just an ugly woman, but I don't know if that's to separate the roles or is how he'd prefer to dress and behave if not for his role in the government (of which you are correct, being a crossdresser or transgender would never fly for a Chinese official).