I'd say he should come short of actually endorsing any candidates or major political parties.
Having policy positions and political positions would be fine, and how they make their way into stories is going to depend on the writer.
He shouldn't actively try to be appear apolitical like in that dredge that was DCU: Decisions. It shouldn't be a secret to the people of the DCU, and us as to what he believes politically.
Like, we know with Wonder Woman, her position on marriage equality is that she favors it from a liberal standpoint. That's in a comic, and made quite clear.
What about Superman though? Does he also favor it from a liberal standpoint? Does he disagree with it from a religious standpoint but still believes it should be legal? Does he not think it should be legal at all? Does he come at it from a queer theory perspective and disagree with on that basis, similar to someone like Michael Warner.
What would be his reaction if Maggie Sawyer invited him to her wedding? We know what the answer would probably be, but lots to explore.
On the economic font, those old Golden Age stories didn't make it a secret that Superman believed in things like regulation, and public housing. DC shouldn't be shying away from it now.
But I think even something as simple as Clark telling Jon that 'An Inconvenient Truth' is a documentary he should watch will anger a lot of people, so if it's a matter of not causing "division", that ship has long sailed.
I'm not doing the idea justice, but that's why I'm not a writer.