So if it was legal for men to go naked in public in public places, would the response by men be any different? Women do tend to be more private about their nudism.
No, the response is exactly the same. In the UK public nudity is legal but neither sex walk around nude despite what some here claim or fantasise about.
Nudist do have organised events such as swims and woodland walks, and they police their own groups to make sure perverts claiming to be nudists are quickly identified and rejected. Sometime reported to the police.
Solo nude (its always men) woodland walkers have a much more difficult time explaining themselves if seen and challenged. Claiming nudity is legal and identifying as a nudist is not the get out of jail free card some here think it is.