This is the cultural relativist's approach. If we were all cultural relativists, though, nothing would ever change because we would have no moral impetus to change.
We've pretty much decided as a society that unwarranted discrimination is bad. I don't particularly see a problem with enforcing cultural change with law in order to move towards a more open society.
Bathrooms were never designed for genders or sexual preferences to begin with. I never understood this issue from the start. They're designed around whichever genital you have on your body. It doesn't matter what you look like or what your claimed "gender" is.
Just change the signs on bathrooms to say Penis or Vagina and be done with it I say.
I'm having a pretty good laugh at how half ass your efforts are if avoiding a store that doesn't actively discriminate against .3% of the US population is how you do it. I assume if you had a son though you'd have no problem with him using the men's room?
I'm frankly baffled though that people can be all like "man this public bathroom was so not awkward before Danny-now-Danielle walked in".
Which is basically just saying you don't agree with the people you don't agree with.
There's been no rash of predators using transgender status as a tool to commit crimes. You people act like Target is changing the status quo and they're not. They're just reaffirming what happens in bathrooms all over the country.
Potentially dangerous? That defines all situations, without exception, given any environment with incomplete information.
Uncomfortable? Maybe. But that's more of a personal problem. People can feel uncomfortable under a plethora of circumstances, many of which are utterly subjective and worse, irrational. I have a feeling that you don't support the idea of 'safe spaces' though, so it's likely that hypocrisy abounds.
That's alright in concept, but I'm talking short-term. We already have millions of bathrooms built for each "gender" (see urinals). You could just slap "Unisex" on both doors but I think that would get an even worse response than the current situation.
Also I think a lot of fears come from the fact that bathrooms are private places. There are no cameras and a lot of them don't see much traffic. People feel vulnerable when they're in there all alone and someone else comes in. You could easily eliminate the fear of sexual assault by just saying "this bathroom is only for people with this genital" IMO (which seems like a reasonable compromise for this whole transgender argument).
Do people forget that unisex bathrooms are a thing? As far as I am aware, we didn't see a spike in harassment when those were introduced in more locations.