I disagree. Shunning (i.e. choosing not to engage with someone) is not incivil. In fact it is a perfectly reasonable thing to do if someone is arguing a position with which you do not wish to engage. If people ignored other posters more... rather than choosing to get outraged, it would be much more civil place.
Once I choose to engage with someone, I intend to be civil. I have no obligation to engage with anyone.
You have no obligation, but if you just shun someone because they hold a certain POV, you are giving them reason to believe that you are biased against their POV so strongly that you are willing to shut them out of democracy completely.
Let's take the example of people who are frustrated with the widespread drug culture and the social and economic effects it has. Duterte is a great example of what happens when the drug industry and its facilitators just ignore its critics. Now people are killing drug dealers without trial, and that would not be happening if the drug industry had been listening to its critics all along.
Many times I read a post and say, this point of view is so ridiculous that it doesn't warrant a response. The 9/11 conspiracy theories are a good example of this, these theories are so insane (in my opinion) that I don't feel wasting any more of my time. I didn't attack the people who hold these theories. I am perfectly willing to discuss other topics with them and I have no problem agreeing with them on other topics when I decide what they are saying makes sense to me.
It isn't incivil for me to say that I find these theories to be without any merit and not even worth arguing. Criticism of an ideological position is not a personal attack, nor is simply choosing to not discuss it.
No, criticism shouldn't be taken personally, nor choosing not to discuss it for personal reasons, i.e. that you are tired of the topic. But when you start to make your choices part of a collective effort to shun all Republicans, or all Trump supporters; that is a highly anti-democratic approach to public discourse. You have the responsibility to listen to different POVs in democracy and reason with them and allow them to reason with you. That is what makes democracy civil instead of being a war of shunning and ideological manipulation that is has largely become.
Think of it the other way around: was it right for anti-civil rights people to shun and ignore civil rights activists instead of listening to them and engaging with them in discussion? Didn't people have a responsibility to listen to what people were saying about racial problems and to engage in a good faith discussion about how to solve those problems in a way that would facilitate peace and prosperity for all?