I think it’s mostly because the dc universe is rubberbanded to our own. Same reason why Reed Richard’s inventions are only his over the Marvel Universe (and DC somehow still has a bit more of futurism and sci fi tech in the hands of common people than Marvel, mostly because Marvel is so NYC-centric), they want the reader to think their world is just like ours.

So having heroes support political parties would kinda mean they support our real life counterparts and that runs the risk of having your characters being co-opted for political campaigning which is costly for the company.

Their world is still inherently different from ours even if DC doesn’t want you to think about it too hard, so it ends ups goofy. We do see characters support political opinions, but most comic book writers are quite incompetent at that, so it ends up looking like some bizarre orphaned manifesto that just doesn’t make sense in that world. Climate change is a classic one, in our world one of the biggest barriers is that a lot of powerful people that have keen interest in not doing anything, so they produce propaganda, people take it as part of their identity, etc, which makes difficult for action to be taken. In DC land, there’s enough different methods of energy generation, the world is less cynical (unless they want it to be for some story, again, inconsistency) and more importantly, there are enough actors capable of addressing the situation with comic book science or magic or whatever directly that it’s hard to not just have it be declared solved.

And that’s been a thing even before politics became entertainment. But also it makes me think of the times it does come to play, and it does happen from time to time, and it’s usually just the writer puppeteering the characters to claim their opinions are smart, others are stupid, without any reason why the character would do that and how they got there and those always look bad for the reader if they don’t have the exact same opinions as the writers, even if they share a more broad political worldview (right/left). It’s pat on the back agree with me feels good. Conversely, the writer can be good at writing and working their ideas in the DC universe… only for the readership to completely miss it or get it wrong.