Here's a modest proposal: the next time you're ready to launch into an entrenched defense of your point of view using some well worn verbal cliche from your favorite talking head, stop. Clamp that mouth shut, reign in those anger-fueled emotions, and listen. Truly hear what the other person has to say. Ask questions that tease out (without creating a defense for you, you clever soul) how the individual really feels and prunes away the verbal clutter of their favorite cliched talking points. Perhaps suggest you get a cup of coffee or tea and every time you feel like jumping in with an angry retort, you take a sip instead. When it is your turn to speak, reasoned, friendly responses about how you see the issue and feel about it (no accusations or demands or belittling language here) is in order.
The idea is to listen more than speak and actually try to create friendships. Friends have far better influence on each other than enemies do. I know many stories of unlikely friendships that have changed entrenched points of view. It is certainly better than throwing verbal bombs and perhaps literal fists at each other (or worse when the blood really boils). What do you say?