In a context where Batman is known and seen through his public League appearances, the misogynistic, homophobic, "alpha male" guys start using his image to illustrate their discourse of going to the gym, and seeking submissive women. They admire and misinterpret his traits as endorsements of their toxic masculinity. Online, they share images of Batman with stuff like "Be the Alpha, Be the Batman". They even use the word Batmen as a synonym to Alpha Male. "Real Batmen don't show weakness".
When Bruce becomes aware of this, he hates it. He despises them for all their messed up views, knowing they completely misunderstand his principles. Batman's true strength lies in his commitment to justice, empathy, and respect for all individuals, values that are fundamentally opposed to the toxic masculinity they promote. Bruce is determined to distance his image from their rhetoric, seeing them as nothing more than sexist and homophobic idiots.
So he decides to be a tiny tiny bit more Brucie when they appear in public. Not in form, but in substance :
When he's asked a question, he tries to go "I have no clue, I'd have to ask Black Canary.", or "I'm not sure, I'd have to see what Wonder Woman thinks about that", or "This time, we really couldn't have done anything, anything at all, without Supergirl."
Also, Batman becomes more visibly affectionate with Superman. During public appearances, if he senses a camera on them, he makes sure to be seen clinging to Superman. He would rather face dating rumors every day than be associated with those idiotic discourses.
(It's also a good premise for a superbat fake-dating fic !!)