I think that if men could menstruate it would be a openly discussed topic. Take a step into barracks and you’ll find that men aren’t very concerned with hiding their bodily movements, farts, burps, dip spit or really any other gross thing they do. The bathrooms in particular are a NSFW story to themselves. Men would openly make fun of each other’s periods and somehow it would come to be an insult just like being a dick is. We’d definitely see an increase in spending into how menstruation works and I think that charting your period would be a really normal thing.
Research into menstrual suppression would be driven by the professional sports leagues. The NFL only has 16 regular season games and they do everything they can to make sure that all of their players are in the best possible condition to perform on those days. Pitchers in baseball take the mound once every five games and are notorious for missing starts due to minor illnesses or even bruised fingers. To maximize performance, I think that professional sports leagues would heavily invest into menstrual suppression so that their athletes can feel in their prime physically and mentally. Even with that I’d be willing to bet that an athletes menstrual cycle would be taken into consideration during contract negotiations almost as a prior injury is today.
Teenage years would be especially difficult for young men if they had a large increase of testosterone every month. Already aggressive teenagers could be very difficult to deal with and I think that fights in middle and high schools would increase if young men didn’t learn to understand when they’re going to be PMSing. Having an app that would track your menstrual cycle would be very common and people would probably talk a lot more about their cycles if both men and women had a menstrual cycle. Since both men and women would be equal in that respect it would be a lot easier to talk about publicly.