Since the only vague summaries are being widely reported and the details are going to matter to many people here, this is where the full text of yesterday’s executive order redefining gender and sex may be found.
Warning: It is worded to be cruel and dehumanizing. If you feel you need to read it, have loved ones and self care prepared to support you.
The bathroom segregation here is go prevent endangering women. But he does not mention how to handle assault in these places or whether that should be different for each gender.