Do women walk around naked in women's restrooms? Are there no doors on the stalls? Do you just sit side by side, chatting with your neighbor?
Indecent exposure is still a crime. Nothing about transgender policy would change that. So what's the problem?
Now, in a men's room, there are urinals. But for some reason, we don't hear about the problem of women standing beside a man at one of those. (Admittedly, I probably wouldn't notice, because I don't look at the people peeing beside me, let alone at their genitals!)
As Trevor Noah points out, we've been here before. We've been here when racists were outraged about the idea of sharing a restroom with a black person. We've been here when homophobes were outraged at the idea of sharing a restroom - or a shower - with a gay person. It's the same thing.
Well, not quite, because transgender people are a tiny fraction of the population. If you're not one of them, chances are good that you will never have a problem or even anything that you could imagine as a problem. Indeed, they've always existed, and we've never had a problem before now. Do you routinely inspect the genitals of every person you share a restroom with?
For transgender people, this is a problem. It's a problem they face every day. But for the rest of us, it's not. For the rest of us, it's just bigotry or acceptance.
PS. If you haven't seen it, I highly recommend this video. Transgender rights haven't been on the radar for most of us for very long. Ignorance is understandable, but can - and should - be corrected.