The problem with this is, you can't fight in two corners at once, especially in the climate we're in (where men and female are in absolutes, politcally); there's nothing that will redefine what masculinity is if the Right already has ahold of that definition with both hands and won't let go. How can the Democrats fight for the equality of women (whilst the opposition is putting men at the forefront), while also fighting for what is masculine?
Trying to divy up their energy, resources and favor between the two means they won't get either women or men on their side. Women will feel they're not at the forefront, and men will feel they're not at the forefront, and then they're in danger of losing both.
And look, the figurehead here for what is masculine is a convicted criminal and known rapist (who exemplifies the benefits of white privlege), so if this is something that these traditional men either ignore or identify with, than what could the Democrats possibly harness to get that demographic on side that won't put a foul taste in the mouths of their supporters who're already fighting against this?