When world views are worlds apart, conversations can be awkward, uncomfortable, and at times, argumentative.
When in this situation, I find the following strategies useful:
I ask questions with genuine interest
I search for common ground and then say:
You're right
I totally agree
When the ground isn't common I'll say:
That's really interesting
I see what you mean
I get what you're saying
I haven't thought about it that way before
And then I might say:
My perspective is slightly different...
I'm with you on that but I've a slightly different take on this...
I'm interested in what you think about this...
It helps to practice on low stakes conversations, when there's little pressure to connect.
Celeste Headlee's TED talk has some excellent insights on having good conversations that I use everyday.
Good luck :-)