After reading _The Righteous Mind_, this is something Jonathan Haidt's book drilled down on me. The book focuses on the political and religious divide in the US primarily, and his Moral Foundation Theory shines some light on the issue: In the case of conservatives vs liberals, their moral matrices are vastly different and that's a recipe for disagreement.
In Moral Foundation Theory [1], Haidt and a group of social psychologists seek to understand the variability of morality across cultures. Despite this variability, they find there are similarities and recurrent themes. They think there at least are six foundations: 1) Harm/care, 2) Fairness/cheating, 3) Loyalty/betraying, 4) Authority/subversion, 5) Sanctity/degradation, and 6) Liberty/oppression.
According to Haidt, liberals (aka leftists, Haidt uses "libertarians" for "classical liberals") respond extremely to the harm/care and liberty/opression foundations, however conservatives do not respond to these foundations as well. In fact, conservatives respond to all the foundations by the same degree while liberals respond to only two foundations. Both liberals and conservatives respond to liberty/oppression but they approach it differently.