Is it okay for a lady(F) to use the gents(M) toilet/s ?

​ I note someone posting earlier about being called to meet their work's HR over a problem caused by their turtle's head, that got me thinking about the following... Twice in recent weeks I've been in a situation where I've gone to use the gents' and been surprised by a lady in there already, I'm a bloke by the way. 1st: I'd been working as a supply teacher in a local school for some weeks. In the male staff loos there are 3 sinks on the LHS, 3 cubicles at the far end. As I battled my way past the key-code lock with arms full of books etc. a person with short afro type hair was finishing hand-washing, turned their face to me & beamed a smile. As they stood and turned I realised to my surprise that they were then quite obviously female. I uttered an 'eh, h, hiii' and continued straight past into a cubicle -all 3 were free. From their lanyard I knew they were also there as a supply teacher and surmised it was their first time at the school. There was a large clear sign on the door consisting of a stick man & wording MALE STAFF. Maybe this lady had EAL, but there are obviously checks on teachers' skills and abilities. 2nd: My first time in this particular town centre bakery / cafe... I popped around the little screen wall to see three doors: ladies, disabled & baby-change, mens. The mens was in use so I stepped back & waited, a few moments later I heard a flush, tap water running, then electric hand dryer going. A few moments later the lock clicked, handle squeaked, and as the door creaked open, out strolled a 60 odd year old lady (short grey hair with a blue rinse, wearing spectacles, and dragging her shopping trolley behind her). As I stepped aside to allow her past I noticed an old bloke arriving around the corner too -he looked more surprised than me by the face he pulled as I raised my eyebrows in mock shock & did a little hand-raise shrug 🤷‍♂️😂 ........................................................ In case No1, in terms of gent's loos, there aren't many around. I had to walk to another school block to use that. Has she not realised, or realised and decided she either couldn't wait or didn't want to walk far to a ladies loo ? In case No2, I can't see why she'd have gone into the gents unless she hadn't realised. Now, back to my post's title... Is it okay for a lady to use the gents as I'm quite sure, by the other post in this sub I referenced, it's NOT generally acceptable when it's a man using the ladies.