Should the gender signs be observed on single cubical public bathrooms?

What I mean is a single closed off bathroom that is suitable for only one person. A lot of coffee shops have them.

To me I don’t really see why they need a gender sign. Since it’s only one person using it and it invades nobodies privacy.

Basically I used one of such public bathrooms in a Starbucks. It was a single person bathroom. There was one single bathroom for men and another one for women. But the male bathroom’s inside lock is loose and tends to unlock. So I wasn’t going to use that out of fear of the door opening while I was doing my business. So I just used the female bathroom.

Anyway as I’m coming out if the bathroom. Some woman remarks in a very snarky kind of way “it’s actually the ladies”.

I just ignored her though and walked off. I kinda felt like saying to her that it really makes no difference who is in a single cubical toilets and to basically get over herself. But that would have resolved nothing and she probably would have got more snarky with me.

What are your thoughts?