This has become quite a public uproar considering it only concerns a very small percentage of the population who identify as something other than what their genetic make-up (remember, biology is also a Science!) was at birth. Hermaphrodites, gender dysphorics, kinky crossdressers, whatever. Fine. They're outliers vs the general "normie" population, and manipulating the law in favor of them vs maintaining the safety and privacy of the rest of the population is abhorrent on face.
That said, I don't even like to piss at a urinal next to some other dude, or take a dump in the office stall next to him when I can smell and hear him destroying his stall. It's just gross, and really anything but(t) private. And don't get me started about people who actually answer their goddamn phone while taking care of nature's business. I even heard a guy dialed in on a teleconference doing it once. He thought he was muted. He wasn't.
The notion of multi-stall unisex bathrooms being open to anyone - the "Ally McBeal" model, which I've yet to see in the real corporate world - is realistically unworkable even if it is appealing in theory. You open minded types who endorse this notion while complaining about "rapey" environments have no idea what you're entertaining: the free reign of genetic males (remember: biology is SCIENCE!) in a dress and heels or not, to access and use your bathrooms while you partially disrobe to let your body do its thing isn't enlightened, it isn't clever, it isn't post-modern hipster PC, it's just fucking dangerous. Think about it.
I'd vote for unisex public bathrooms only if they're individual like you'd find in a person's house, i.e. commode and sink, and most importantly, a door that locks. We're starting to see this happen in some bars and restaurants. Target and many grocery stores have tertiary "family" restrooms where people can take opposite sex young relatives for potty assistance, diaper changing etc with the safety of a locking door. Dressing rooms are already unisex (though usually supervised). It's just more practical and as others have pointed out, efficient vs long lines at men's or women's restrooms while the others happen to be near- or actually empty.
TL;dr: "Multi-sex" bathrooms aren't safe, or practical. BUT unisex single-occupant (or "family") ones might be, in the long run.