I've been thinking of it for a bit - and I'm pretty sure the answer is with some amount of nuance, but legislatively left since his family was big on public works and he honors his parents above all.
Batman doesn't desire a police state, but he will monitor everyone himself.
He's flat-out against guns, though I'm unsure if it's ever stated if he's against the 2nd amendment.
He surely believes in combatting climate change.
He's the biggest employer in Gotham, but also probably is the most fair with wages in Gotham.
He works with the police, but also works against police corruption.
He amasses fortune through business - but uses that fortune to provide a public service - in the form of a private militia.
Ultimately, what I think it comes down to is this: public works that benefit society make his job as Batman easier and closer to unnecessary. He's about helping people, and not so much "pull myself up by my bootstraps". Like, there's no argument that Batman would support systems that help the poor and disenfranchised.
If a candidate was personally a problem, he would identify them and probably remove them from contention before voting became a thing. In the case of Trump, he probably is able to access whatever records exist that prove Trump as a pedo-rapist and doing shady deals for foreign actors and then reveals that publicly to bring him down. If it's just a politician he doesn't like, however, then he'd just vote against.
Ultimately though, I don't think Batman cares about voting as much. It's more likely he masquerades as a bigwig donor - probably for both sides to play the role of buffoon - and understands that a presidential choice doesn't always have anything to do with the work he considers that he has to do himself - which is, ultimately, very authoritarian at times. He's a moral absolutist, after all.
Of course, Batman has been personally named public enemy number 1 by a president before, so I'm sure he has some care for who takes the office beyond what we do.
I'll defer to this evaluation. I've really only got surface-level Batman knowledge.
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"God Hand is the ultimate expression of the joy of humanity, specifically the punching part of the joy of humanity."-Shigeru Miyamoto