This episode of Bones commits one of the worst tropes of bad writing: when you're trying to write characters with diametrically opposite beliefs to you, but you can't rebut their main arguments (and you don't want the audience to sympathise with the "wrong" side), simply make them say the most sociopathic things to repulse the audience.
MRA groups do attract people with fringe beliefs. Some of them are incels, some are men who've been through rough divorces, but there are MRA ideas that are worth of discussion (which Brennan actually concedes). No matter, make the horrible men sl*tshame women and ask them to be muzzled to let the audience know they don't have to wrestle with those ideas.
The Booth gambling storyline from Season 10 was already dumb, Bones goes back to that well now by making Hodgins an a-hole to everyone around him. As other reviews have pointed out, this is simply drawing up a villain arc for the sake of ratings rather than a sincere attempt to dramatise how a person or two people in the case of Angela would deal with an event like this.
Bones is hardly the worst offender for moralising against the obvious ideological opponents of the showrunners, but they rarely stick the landing when they do, and this episode may be the worst example.