@Searcher,
If you need to talk to them about it (i.e., they corner you / badger you), use the Socratic Method. That's where you just ask leading questions about the person's beliefs, statements, positions, etc.:
Socrates, the early Greek philosopher and teacher, believed that disciplined and thoughtful questioning enabled the student to logically examine and validat ...
cetl.uconn.edu
Like Skills said this will get them elaborating on their viewpoints. You never reveal your own. At most you just say, "Hmm that's interesting," and ask more questions. Depending on your goal you can just ask questions until you reach the point where they reveal they have no idea what they're talking about -- but I wouldn't advise that for the workplace. You'll just make enemies (the Athenian elites poisoned Socrates with hemlock after he pissed them off enough with his question-asking!).
Personally with agitated political people I will ask a few questions like this to get them to explain their views a bit, basically just bring them to the precipice to where they start to feel uncertain about what they're saying, then I will change the subject. Gets them off their high horse, but avoids robbing them of face; the topic change lets them save face, so they end up being grateful. They also realize that talking to you about politics risks exposing them as idiots so they refrain from bringing it up with you again in the future and just stick to more agreeable subjects.
(so for me the technique is: don't go all the way into making them feel like idiots, just bring them close enough to it that they can feel that talking to you anymore about this would be a bad idea for their face)
Otherwise, if you do NOT need to talk to them (i.e., they are not badgering you or cornering you), and it's just bugging you listening to it, it helps to understand Jonathan Haidt's
Moral Foundations Theory:
e.g., if they are liberal and you are conservative, you will value
- Care/harm
- Fairness/cheating
- Loyalty/betrayal
- Authority/subversion
- Sanctity/degradation
- Liberty/oppression
Meanwhile they will ONLY value
- Care/harm
- Fairness/cheating
You both have equivalent amounts of "fucks to give", but yours are distributed among six categories of values while theirs are concentrated into two. To your ears they will be OVEREMPHASIZING the importance of those two while seeming morally bankrupt on the other six; to their ears (if you start spouting politics back) you will have weirdly misplaced values on values spectrums that TO THEM are not even moral dimensions at all; meanwhile you will not value the two moral foundations that to them are the only ones that actually matter nearly enough, which makes YOU seem "morally bankrupt."
This is a largely unbridgeable gulf, because you cannot get them to view your extra values as "moral values" except in the abstract, and only if they are very open-minded (most people aren't). So it is better just to understand that people with opposing views to yours are simply operating from a different set of morality
at a foundational level and there's no point trying to argue with them about surface-level politics. You'd have to totally change their moral foundations first, which you almost certainly cannot (i.e., your first task before you deal with superficial politics is to get Mr. Liberal to decide it is important to respect authority, honor loyalty, maintain purity, and value liberty. You will not succeed at that, which makes the superficial conversation moot).
Once you understand it then you can just shrug, because that conversation is irrelevant to you.
Also, arguing politics with peons is just totally pointless, unless you work in a Senator's office or something. If you could change their minds, would that change your government's policy? Unlikely! So it's just a colossal waste of time and productive energy.
Chase