Civility is the practice of maintaining civic good relations, where civic good relations are those relations that make society 'work' in some sense. (The old Aristotelian name for them would be civic friendships.) Society is a way in which we live together, and civic good relations are those relations among the people in society which make living together possible and viable, either because they are pleasant, or because they are useful, or because they are good for us. In this sense you can have civic good relations with people you don't really like at all; in such cases you simply recognize that, whatever problems you have with them, you have to live with them to achieve certain good things, and you act accordingly.
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All the mechanisms of democratic politics depend for their success on reliable venues for rhetorical communication; good rhetorical communication will often require argument. But you can have a pretty successful democratic politics based less on argument than on human sympathy, and one finds in fact in democratic politics that resolution of serious disputes is very often resolved not by argument but by compromise or by mutual sympathy or by a live-and-let-live approach. We should certainly be thankful for that; otherwise our societies would have failed long ago.Of course it's election season again, and there have been a few uncomfortable culture-war flare-ups already. I'd lament the intensity of the polarization, but I'm actually not convinced that we're anywhere near a high-tide of civic division. On the other hand, social networks do give us new modes of engagement, and it's not clear that the old practices that sustain a civil society transfer easily to the highly performative world of social media.
UPDATE: Read the good comment.