My father is very conservative on most issues, where I am very liberal on most issues. We still get along perfectly because politics is not that important. He's still my dad, still a great person, and still an exceedingly good debater.
I think the primary source of Americans' anger is the disrespect for other peoples' opinions that's spoon fed into us 24x7 by the mass media, who cares much less for civil discourse than a good fistfight that attracts more viewers.
The rise in America's anti-populism starts with the rise of broadcast hate speech, IMHO.