Today I emailed one of my favorite style bloggers, explaining that I'm about to buy my first pair of spectators, and asking for advice on how to polish them.
He advised polishing only the colored portions, taking care not to even get close to the lighter (usually white) portions.
I didn't ask for elaboration, so what follows are my thoughts.
That makes sense, because generally, the two portions of a shoe that need polishing most are the sole edges and the toe box; the edges are what get dirtiest, and the toe box is where most scuffs occur. Since the edges usually run up against some of the lighter portions, you could take extra care to use a neutral edge dressing or shoe cream for those.
It's probably best to leave the lighter (usually white) portions alone unless they become noticeably dirty or scuffed. Then, if they're calf, you could carefully use a white polish only on the scuffed portions, taking care to avoid the edges of those sections where they meet the darker portions. If they're suede, you could probably carefully apply a little of the contents of a buck bag, which is a bag of white powder used to clean white bucks. If they're mesh, you could try cleaning them with a clean cloth, dampened with water.