Sigh. This nonsense again.
No, a sign doesn't stop men with bad intent coming in.
It does, however, stop decent men coming in - they see the sign and respect it.
Therefore, with signs, any men with ill intent will be obvious by their presence.
And, if you can easily identify those who likely have ill intent then you have a much better chance of removing yourself from the situation before something bad happens - or telling security that there is a man in the ladies and getting them removed.
Also, they have to have serious ill intent to ignore the sign. Signs put off the opportunists too.
If all men are invited in, then the creeps, pervs, hidden camera wankers and rapists are given cover.
It's a no brainer. If you care in the slightest about the wellbeing of women and girls, keep single sex facilities.