I don't buy that, and even if they were really appealing to catcallers, fighters, and bullies, they don't have the credibility to do that either. These aren't counselors, clergymen, or teachers. They're marketing hacks for a company that sells razor blades. I don't think they care, and I don't think those men care what a razor blade company thinks. If I was one of those guys, I wouldn't stop because the people who sell me razors think it's uncool (or more accurately, pretend to care about it to get positive PR).
Could there be an internal angle? Maybe. Neither of us can possibly know that.
Gillette is simply following the politically correct model. They didn't make it up. Others did, and their agenda is broader than the catcallers, fighters, and bullies.
I'm not a fan for two reasons. First, I think it's largely phony. These are business decisions, not true statements of morality, and they shouldn't be. Gillette's job is to sell razors, not stomp out "toxic masculinity." Second, I think we politicize way too much, and corporate virtue signaling adds to that. We're running out of non-political zones, and just from a cultural and social standpoint, that's a bad thing.