Any argument here about privacy is entirely independent of sex and gender. Prison is dehumanizing, address that. Don't be a transphobe.
Edit: There's a bunch of mistaken comments here assuming that this will protect women prisoners in some capacity. That's totally wrong! Women in prison are sexually assaulted, raped, and even impregnated by men all the time and have been for years. Those men are guards[0]. And this happens at a vastly higher rate per capita and overall than any assault by trans inmates. Anyone here with a legitimate interest in protecting women in prison would be attempting to address that harm, because it is far more dire for numerous reasons.
[0]: https://ktla.com/news/nationworld/the-rape-club-womens-priso...