Almost every problem that liberals and conservative fight over is a pancakes vs waffles problem.
Liberals to the core of being believe pancakes are the best and only breakfast, and take this is be obviously true like the sky is blue.
Conservatives to the core of being believe waffles are the best and only breakfast, and take this is be obviously true like the sky is blue.
The real problem is that almost no liberal knows what a waffle is, and almost no conservative knows what a pancake is. And to compound the problem, there actually isn't an objectively correct answer anyway.
I think that while it's true that in many cases opposing ideological sides optimize for different goals, and that these goals are not always clearly and openly stated, it's not true they never understand each other. Sometimes they do understand each other, but reject the other side's goals as immoral, unsound, or mistaken.
You cannot simply chalk it up to misunderstanding.
I would say this is a too-comfortable, and obviously mistaken view. There are cases that are obviously about facts, where there are obvious right answers, that are polarized in terms of who believes what.
The best examples off the top of my head are left-wing beliefs that George W. Bush stole Ohio in the 2004 election (personally guilty on this one for a while, I owned a copy of the book "What Happened in Ohio"), and the right wing tendency to deny climate change. No amount of pancakes vs. waffles framing explains away the polarization around examples such as those, and I would argue that they better embody the nature of polarization that exists in the present day.
Almost every problem, not every problem. I know it's hand wavy, but the biases listed on the site capture these large classes of issues well (Libertarian vs Regulatory, Market vs State, etc.), and the foundational beliefs that guide what side liberals and conservatives fall on for given issues are pretty clear if you can level head your way through them.
Respectfully, I don't even know if I would agree with that on a number of levels. Even the existence of one example should have stopped you in your tracks already, because that's all it takes to demonstrate as a principle that bias doesn't work that way. But I also think those are just the tip of the iceberg, and there are broad swaths of widely believed claims that are fundamental to people's sense of their own political identity also in exactly this unfortunate category.
On the left side of things some (not many but some) there's a lot of apologizing for and minimizing of the horrific human rights records of the U.S.S.R. and China, some degree of falling for present day pro-Russia misinformation, and uncomfortable truths about the party's own closing ranks around people with a history of sexual abuse. And on the right there's a lot of deep-in-the-bones denial of evolution, or historical revisionism about their ties to the "party of Lincoln", or who won the 2020 election, and it's expanding every day to include new topics like prediction of hurricane paths to provably wrong information about nutrition, and so on.
I would say it's so omnipresently pervasive in the present day that it's impossible to wave away and is increasingly fundamental to explaining and understanding polarization.
I think we are maybe talking about different things. Liberals and conservatives have wide platforms that cover hundreds if not thousands of topics, the thousands and thousands of policy decisions needed to govern a full society. It's not just 3 or 4 things that get lots of attention at any given time, because we can shape any narrative we want without looking at the full picture.
I can say Bernie supports tariffs so he is a conservative and Trump is giving student loan relief so he is liberal. Both are true and obviously those ideologies are not theirs, but these anomalies exist in an ocean of policy decisions they adhere to, the ocean which defines their actual bias. Look at the forest of policy decisions here, not the individual trees.
Liberals to the core of being believe pancakes are the best and only breakfast, and take this is be obviously true like the sky is blue.
Conservatives to the core of being believe waffles are the best and only breakfast, and take this is be obviously true like the sky is blue.
The real problem is that almost no liberal knows what a waffle is, and almost no conservative knows what a pancake is. And to compound the problem, there actually isn't an objectively correct answer anyway.