I've been thinking a lot about this lately. There are a few different aspects of it, as far as I can see.
First is how you present yourself as an educator to the world and other educators. I'm pretty active on Twitter for largely educational purposes, and except for rare occasions I like to keep politics out of my tweets. I will comment on political conversations on education, but I try to make them centered in educational concerns rather than partisan concerns. For me, staying non-partisan as a publicly employed educator is an important representation of the profession.
Lately, I've wanted to be more politically active, as I feel that speaking out is important. For that, I've created a second Twitter account that is solely centered on my political views. By having two accounts, I'm hopeful to make things work. We'll see how it goes.
In terms of classroom practice, I really like Jon's comments about the importance of teaching an understanding of how to do effective research, to seek for the truth, to communicate with others, etc. I think if education on the whole did a better job at this our county might be a lot less polarized. There are non-partisan principles that every citizen should understand, and I have no problems bring those sorts of conversations and study into the right places in academic work.