Ignoring that most games aren't masculine... the general attitude suggests that men wouldn't care.
So you really shouldn't ask "What would you do if it was flipped?" when men do not have their own "things" (Most guys don't consider games a "Guy thing", only so much that a lot of guys play it) but recognize that women in fact do "have their own things" that men aren't allowed to participate in, without odd looks, and this is the accepted reality.
There are some things that are actually outside male privilege.
People have, in this thread, argued against inclusiveness
They have argued against inclusiveness for inclusiveness sake. Or rather against forced or artificial inclusiveness (AKA: Kids Show inclusiveness!)
Preferring it to happen organically and over time. Over pressing the issue. Them wanting games to change because people's tastes change rather then because people are pressing the issue.
But people are shortsighted, and video games in particular have had to withstand a lot of attacks in recent memory
Well not just videogames. A lot of gamers are also part of "nerd culture" (or Geek Culture) which itself has been demonized several times. Such as the whole "Dungeons and dragons is Satanic" thing that was so large I was surprised me parents actually referenced it when I told them I played it... Or Rock and Roll, or Rap, or *keeps going*. Basically culture isn't very nice to niche groups with interests that the general public do not understand... and Indeed a lot of the criticisms brought forth towards games are often done without an understanding of the medium.
As well unlike most things Videogames are not protected under the belief that it is an artform. Thus people do not respect its artistic integrity in general, so criticism has a lot more impact because it is more of a criticism against the genre itself. Mind you this is changing, but you don't see anyone legally protecting the right for a game's artistic statements.