I'm 6 foot and easily read but I've lived in role for two years, have always used female restrooms (in the UK) and not yet had a single incident.
There, more than anywhere else, it's important to look confident and at ease.
It's a lot easier if you are accompanied by someone who is clearly a genetic female though and many times I have been.
If possible, when going in alone I watch the traffic for a few minutes and try and pick up on when the place is empty or near empty - the worst possible situation IMO is to walk in and find a queue 'cos they'll all have plenty of time to notice and study you
- The going in part is the difficult one - once you're in the stall you're safe and even if the place is crowded when you come out, you're on your way OUT then so who cares? 🙂
Part of the "problem" is that the ladies room is NOTHING like the Gents - girls loiter and chat to each other even if they're complete strangers.
There is one pub that I go into that has a beautifully fitted-out restroom - complete with a pair of large leather sofas!!!
I walked in there one night, having studied the traffic and concluded that there was unlikely to be anyone else in there, to find SEVEN girls sat on the sofas chatting

- they all looked up at me as I walked in so I smiled slightly and went into the stall. They carried on with their chatter and I did not hear any whispering or negative comment.
It's bound to happen that there will be an incident one day and I have a pre-planned outline of what to say, but...... so far, so good.
I can't stress enough though how vital it is to appear confident and at ease.