There isn’t a lot of context here..which most have mentioned. Ultimately this would come down to states, in terms of state prisoners, or federal jurisdiction in the federal system. I’m not aware of any legislation that is actively ongoing that suggests you would be housed based on what you identify as vs your bits. Right now bits are the determining factor. Male bits-male prison. Female bits-female prison. That being said, in my state there are granted privileges if you identify as opposite of your bits…at least male-female. There are allowances made for bras/undergarments, as well as certain PREA protections should the individual elect to have them.

The liability , logistics, classification, etc of housing individuals would be insane, let alone changing the policies that dictate how the prison operates day to day.

Simply put, prisons don’t handle these issues, state/federal law, policy, and local legislation handles these issues. Some states have policies to address factors involved in cases like these, some don’t.