It’s pretty easy to point to closed-minded Liberals–my exwife is one. Anything to do with the Abrahamic religions was evil, everything pagan was green and good. Any aversion to homosexuality, even if was just on the level of aesthetics, meant you hate fags and were therefore a despicable human being. Accumulating anything like personal wealth is wrong and greedy–this includes things like emergency savings. I’m just picking on her, but I’ve known lots of people who held beliefs like this and would suffer no explanation of opposing positions, and would certainly not validate them. That’s pretty closed-minded.
That said, I think it’s entirely viable to view religion of any kind as limiting; that we as a society could bridge many gaps just by being more charitable with money and tolerance; and that we could do worse than to remember Plato’s often ignored thought:“Be kind, for everyone you meet is fighting a great battle.” Simply acknowledge that there are roughly 7 billion ways to view the world and one’s role in it, and as many sets of priorities.
I consider myself a liberal simply because I lean a bit to the left socially. For the most part I want everyone to just leave everyone else alone to do their thing and experience this planet in a way that brings them joy. I think that’s fairly open minded. To the extent social conservatives can hold true to their own beliefs and not foist them upon others I think they too can be open-minded.