Comics

Keep in mind that if he were real they would not know that Bruce and Bats are the same person. So they wouldnt know he's a billionaire.

Also keep in mind that depending on the version/portrayal, Bruce Wayne does a fair amount of anti-poverty stuff in Gotham. But "Would they like Bruce Wayne" is a side question here.

Also keep in mind, that the best way to answer this question is to assume all of Gotham comes with him, otherwise its a completly different question for two reasons

1. Theres no supervillians irl
2. Real world police departments would not be cooperative with him like Jim Gordon is.

So to have a Batman that is fundementally the same as the comics, we have have most of the rest of Gotham so those two things are the same.

This means that he's not just beating up poor people. He's fighting mass murderous supervillians. He's breaking up organized crime. He's exposing police corruption (he does this last thing a lot lol). And most of the poor people he "beats up" are like, muggers who are victimizing other poor people. He also does dumb shit like stop bank robberies, but lets keep the full scope in mind here. Hell if we bring the entire DCU with him, then he's also a member of the Justice League and regularly saving the world from destruction lol.

I largely agree, I think, that real world Republicans would like real world Batman, but I want to make sure you understand all the nuance of the question and arent opperating on a surface level understanding of the character and his world.