Scott Aikin and Robert Talisse argue that while civility is vital in democratic societies, "the relevant kind of respect is not that of the calm tone and cool demeanor" but instead "has to do with the ways in which we acknowledge our fundamental equality as sharers in self-government":
The moral core of democracy consists in the project of enabling citizens to live together socially as equals, despite the fact that they disagree deeply about fundamental moral and religious matters. This democratic moral vision can be realized only when citizens recognize a duty to respect each other as fellow citizens, equal sharers in political power. This respect requires citizens to recognize what John Rawls called the duty of civility, which is the duty to offer one’s fellow citizens public reasons when deliberating with them about the public good. Knowing that deliberation occurs against the backdrop of deep disagreement, we must on the one hand be willing to recognize the diversity of religious, philosophical, and ethical commitments available to democratic citizens. On the other hand, we must be able to explain the basis for any policy we advocate with reasons we can expect any of those diverse individuals to endorse as consistent with their status as a fellow free and equal citizen. That’s the tightrope of democratic justification. Democratic deliberation, then, requires us to argue from a public perspective.
Previous Dish coverage of their thoughts on respect and civility here.