My dad's parents are Democrats and Catholic, whereas after he and my mom got married he swung away from both of those and became a Republican and more or less thoroughly Protestant (nominally Methodist like my mom's family, but influenced by a bunch of the Baptist and Dispensationalist preachers on AM Radio). He generally tries to simply overlook those differences but sometimes gets dragged into those heated rants if it turns to politics.
I, on the other hand, was raised with those elements in place, but almost contradictorily, my family also stressed centrism (or moreover, 'vote for the one that you think will do the best job, not just because they belong to your party', and equally held respect for both FDR and Reagan). I sharply swung away from the religious underpinnings we were raised with, and came out pretty thoroughly Methodist rather than just nominally - however, I'm also ecumenical in that I don't share any sort of conviction that Catholics are wrong at all (my disagreements mainly concern the question of validity - I hold to multiple validity because I see Protestantism as part of greater orthodox belief). I remember that when I actually came out and said I was a preterist and didn't agree with such things as the Rapture my dad retorted with 'don't you take anything in Scripture literally?' From that point on I just decided it was easier to try and ignore it and not bring it up unless it was way too blatant, which hasn't really happened yet - I have enough on my plate just attempting to choke down my irritation with dispensationalism whenever that rears its head.
My interest in the history of the Church and getting back to tradition made me 'liberal up' by the standards we were raised with. That's also what happened politically - my opinions are broadly reformist with left libertarian/Old Progressivist undercurrents, which deviate from the almost rank-and-file middle Republican, conversative household I was raised in. Likewise, I don't agree with the sort of rhetoric from staunch liberals that there are no redeeming qualities in the other side, or with social democratic talking points just because. That's why I'm a registered Moderate, not a registered Democrat (even if the Democratic Party is kind of becoming a big tent these days). I really don't think tangible, lasting change will occur until we break out of this two-party system.
So with all that considered, I don't mind trying to play peacemaker, but not in my own family - that's a minefield I don't really want to approach.