Batman was never supposed to be political. His entire appeal is that he was a vigilante who simply had the money, tech and ability to carry out the justice against criminals that many ordinary people fantasize about.
He acts alone usually because he does not want to put responsibility on others, even the police whom he helps
He uses intelligence and skill that he refined through practice
He does not kill, not because of some bullshit like;
>"If you kill a killer the number of killers in the world remains the same"
but because he doesn't want to stoop to that level.
That is why his enemies have always been so interesting, they're all reflections of himself and human nature of one kind or another.
Two-Face - the dichotomy of choice
Joker - madness and impulsiveness caused by isolation
Scarecrow - utilization of fear
Hugo Strange - obsession
Penguin - a craving for opulence and respect
So on and so forth. Many of his foes also crave revenge and their own twisted justice.
In other words Batman when not linked the rest of the mess that is the DCU, is less about political ideology and more about individual human struggle and thoughts.
His enemy Joker is best, not when giggling madly over a clown-shaped gun but when he points out how Batman is not really so different from him: A freak in a suit operating outside the law. He's not a hero but an anti-hero. His fundamental humanity and position as a rich but kind person makes it hard for him to understand that the capitalist system is what creates most criminals he fights and his own status as a billionaire contributes to this. Instead he tries to take the world on his shoulders, but as a mere individual, even a billionaire, he fails because vigilantism is just picking at the symptoms and not the causes; missing the forest for the trees
Batman doesn't work in a world of superheroes like Superman or Wonderwoman or The Flash, He performs above human average because of money, intellect and training, but he is still human, which meshes terribly with superbeings. Being part of shit like the Justice League just makes him a poor parody and infects his character with american comic-book ideology, which is where the whole issue with him being an antihero comes up. He is neither ruthless enough to go full-assassin and thus be a counter to Superman's boyscout ideology yet his own original character contradicts such ideological action as well.
TL;DR: Batman outside of superhero DC-verse is a vigilante anti-hero whose tech and actions are a power-fantasy, and whose enemies are a reflection of himself and human nature.
His inherent characterization is not focused on the bourgeoisie-proletariat interaction, and was not originally political. Thus his character is inconsistent as part of the "American justice and freedom" superheroes of DCU.
For a socio-political/ideological analysis, Joker (especially the recent titular movie) is a much better character. Batman is more of a character study in a detective noir setting, except the private eye is a billionaire recluse with trauma and guilt. Marxist analysis of him can be done, but is comparatively pointless.