I'm interested in how people handle religious & political differences among family and friends.

I have family members with very different beliefs and values.

Many times they simply don;t engage me, or I them

For others we have "off limits" topics.

Pretty much the same here. I have family members who are holeeeee rollers. I let them speak their minds, and don't offer my opinions. Me and my mom have certain topics that are absolutely off limits. Politics especially. She asked me if i voted for G Dub, i about choked.
Among friends, i try to maintain an open mind. But ya know, they are my friends, so, we see eye to eye on quite a bit. If we disagree, i simply agree to disagree and let it go.

If i'm meeting new people, i listen and watch for certain words or phrases, then proceed with caution.

The majority of my family is republican. They talk. I ignore. They ask my opinion, I say I have none. I have said my opinion in the past, and things have gotten out of hand, so I just don't say anything anymore.

Religion... My parents go to a Methodist Church. Fairly liberal church. Still, it's church! I allow them to make their recommendations for me to go to church, I hear their stories... I say, "thanks for the recommendations, I will think about it." and I leave it at that. No arguments... I hate arguing with my family.

Now, if someone I don't even know brings up something that I'd like to discuss political or religious, I don't mind putting my $0.02 worth in. But not when someone is trying to persuade me to believe their beliefs. I prefer to just discuss the differences, and hear out others' points of view!

The overly religious side of my family disowned me when I came out, so I've got no real worries there, anymore.

you wisely barter your partner's renouncing of whatever lunatic beliefs you are bothered by against yourself renouncing your neo-fascist tendency. works. a double victory. esp if at your saner moments you have had flashes of understanding neo-fascism is a load of crap and have felt down about it. and if the belief system you are bothered by probably had served as a factor in you considering fascism first place.