When most people think of "civil conversations", it refers to the way people interact with each other, not how they refer to people not present, particularly public figures. 

So one can be between friends watching television, and have a perfectly civil conversation exchanging nasty comments about the people on the screen, one's relatives not present, the neighbours, etc. That's what normal conversation is like. It is one's democratic right to severely criticize people in authority over us, even make nasty comments about them. That includes not only politicians, but anyone who has been given a platform to preach to us, as journalists are, or public figures of every type. But now we have these conversations online.

An uncivil exchange is when people are rude to the people they are exchanging with.  It prevents honest exchange about those people not present. That does not happen often in real life, unlike social media, precisely because it is more difficult in person.