My experience has been similar, but as long as you're not interested in "winning," you can still have enjoyable discussions.
When I find someone who is inflexible on their position, I ask questions about the things that lead them to hold their position. Often the conclusion is sacred, but not the means of getting there; it may be okay to ask them to explain their premises. Either I learn something that I missed, or I get to learn a bit about how others think.