I pretty much agree with everything you just said here. I think one of the difficult things for us to do, is appreciate the perspectives from other people. I don't mean appreciate like we would a gift, but appreciate as in understanding the nature of something. It's very easy for us to have a kneejerk reaction where because we outright reject someone else's axiom, we are tempted to find their perspective completely without merit and unworthy of consideration.
In some instances, this is really true. If the axiom that someone holds is completely toxic that the logic that stems from it is additionally toxic, we should reject the logic. Sometimes though, it's not true. For example, even though I'm not a Buddhist and I don't believe in Karma, I am still capable of appreciating the concept of Karma, how it feeds into their notions of spiritual development and morality, and how it can and cannot inform my perspective of any statement they have to make where Karma might be a core concept in that argument.
If I metaphorically plug my ears and say "Lalala! Karma is dumb! Reincarnation is wrong! The progress of the human soul is linear and only goes in one direction! You're wrong!" I've put a severe hampering on the conversation and possibly the relationship of the person I'm conversing with. Where as, if I say, "I don't believe in Karma the way you do, but I see why you object to the idea of factory farming when you view the subject through the lens of your belief" all of the sudden the conversation goes better and I find myself looking at an old argument, through a new lens, potentially deepening my understanding of said argument and my personal position on it.
This applies in a lot of areas, not just religious, from personal relationships to public policies.