Socially speaking, I would say that conservatives were generally fair game to make fun of or put down in some way most of the time. Sometimes it would be making fun of rednecks or hillbillies or maybe the Amish. Luddites were fair game to be made fun of. Oftentimes it was less about humor and put downs, but more about moral superiority. This was just my experience, and I'm sure other liberal/progressive/whatever people are struggling to feel accepted in their conservative social circle.
Now that I'm conservative, I talk a lot less about what I think in mixed company. It's simply too risky.
I'm not too surprised that you find conservative arguments unconvincing. In general, purely based on reasoning, I find liberal arguments to be a bit better (on average). Sometimes, they are a lot better. The question for me, is how much weight to put on reasoning. How much value does reasoning have? My personal experience is that reasoning works well for writing software or fixing a bug. It doesn't work as well when I try to use it to decide how I should run my life. In fact, my own reasoning has led me into the pits of hell. That changed my perspective, quite a bit!
I truly hope that you and your friends and coworkers can keep peace and good will towards each other.
> For instance,when conservatives express binding-foundation moral concerns about gay marriage—e.g., that it subverts traditional gender roles and family structures—liberals may have difficulty perceiving any moral value in such traditional arrangements and therefore conclude that conservatives are motivated by simple homophobia, untempered by concerns about fairness, equality, and rights.
This, for instance, seems to boil down to an appeal to authority or appeal to tradition, which, yes, is in the name "conservative" but seems quite circular to use as a reason to hold the position.
"Your position is reasonable on the basis of the dimensions it considers but it fails to consider these other important dimensions" is also MILES away from how popular conservative pundits represent liberal positions.