I actually expect that the opposite might happen and that men going topless in public will be as women are now. Maybe not illegal, but less socially acceptable.
The reason I say that is I've noticed a lot of men (not boys) swimming in shirts, and I've also witnessed people telling men to put on a shirt (or otherwise complaining about how gross it is) at outdoor gatherings, whereas, this used to be extremely common. Maybe it is different in California or Florida.
Anecdotally, I live in a neighborhood of Manhattan know for starting national and global fashion trends, and the trend has absolutely been towards far more skin for all genders and body types. In fact, heavier people showing more skin has been one of the most obvious trends. That and the shrinking number of women who wear bras.
Obviously this is highly culturally variable - in the UK I wouldn't say it has much of a 'socially acceptable' starting point, it's certainly a marker of social class.
Of course, it might help that we don't have that many days a year when anyone would want to.
(Beach or swimming pool is another matter - I can't echo your experience there, but it is quite a while since I've been to either, so can't really comment I suppose. Above I mean 'in public' in general, shopping or walking down the street etc.)
The reason I say that is I've noticed a lot of men (not boys) swimming in shirts, and I've also witnessed people telling men to put on a shirt (or otherwise complaining about how gross it is) at outdoor gatherings, whereas, this used to be extremely common. Maybe it is different in California or Florida.