I have this long running joke with my gf that's kinda related. We joke about an American right wing Batman called "The White Knight". And he specifically targets those the right wing targets. He's always watching above when pride parades pass through the streets. He only looks for criminal undergrounds at gay bars. Instead of consulting Oracle for info, he consults "Q". Gordon is instead a police union boss, and the "corruption" they fight together is the state government investigating police brutality. He listens to AM radio and believes "caravans" of migrants are making their way all to way to Gotham. The Joker is just anyone with dyed hair and makeup (me). It goes on and on.

But to really answer, I think it's nuanced. It really depends on who the villains are. In Batman, the villains are not realistic. They are campy, ludicrous. But if Batman was real, and the world is the same as it was today, who would Batman go after? The closest thing we have to comic book villains are Wall Street fucks, venture capitalists, landlords. If he targeted those people, he might be cheered on by the left, and derided by the right.

Of course, he could use his Billions of dollars to help better than Batman ever could. But maybe Bruce Wayne being a rich douchebag is how he keeps his identity secret, "no way that guy could be Batman"

But if there is no Bruce, and there is just a masked figure who never reveals his identity, targets those real life villains that I mentioned above; I think he might see some support on the left.