While I have been wrong about this stuff before, this seems like a really stupid marketing move for Gillette. It seems to me that the majority of their "user base" is "average guys" who just shave because they have to, choose some disposable that works for them, and that's that. They are sports game on Saturdays, likely blue collar, and somewhat apolitical.
Hitting them with the "men are bad" thing is not going to endear them to Gillette. It's going to likely make them political enough to react in the way many of us do when we are nagged by the SJW scolds.
The kind of guy that will embrace this is a hipster beardy, or somebody that uses some classic or whatever hip shaving technique*, and they aren't buying Gillette products anyway.
*Full disclosure, I'm a safety razor and once in a while straight razor guy myself. I just have a pretty much rest of my life supply Israeli blades, so will also never buy a Gillette razor or blades.