https://journals.sagepub.com/doi/full/10.1177/01461672231198...
It also mentions a 2017 article in The Atlantic that I wasn't able to dig up.
Jonathan Haidt in his book "Righteous Mind" https://righteousmind.com/
The strong left-leaning bias in the sample makes me suspicious that this sample isn't representative of the wider population. I can't find the raw data, but given the selection method I strongly suspect that the sample is mostly college students.
If so, one hypothesis that might explain the results is that conservatives who go to college of necessity have a stronger understanding of the other side than liberals because they're the minority on campus for many years. If you repeated this study with a more representative sample of conservatives, including conservatives who do not have the opportunity to interact with many liberals, do you get different results?
But what is usually meant by "conservatives" are intellectual conservatives, similar again to intellectual liberals who write for the NY Times and NPR. There's an old saying, "if you are not a [liberal/socialist] when you are young, you have no heart; if you are not a [conservative/capitalist] when you are older, you have no brain." Obviously, no leftist wants to agree they're all heart and no brain, but the saying exists nonetheless, from multiple observers; and perhaps in that adage is the same "common sense": if that's some sort of common progression, we can see that those conservatives might very well understand liberalism better than the liberals in that formulation would correspondingly understand conservatism.
However, if you control for intellectualism, either by restricting both pools to intellectuals or expanding both pools to include everyone who identifies as left/right of center, that difference disappears. Neither wing understands the other very well at all, both sides as a rule choose to engage with strawmen versions of their opposition, and each side claims that its strawman is a more truthful model than the other's.
I think the only predictor of understanding is the amount of exposure that someone has to actual human beings who hold the opposing view. Intellectual conservatives may have a slight advantage in this regard because college campuses tend to lean left, but I've interacted with plenty of college-educated conservatives who buy fully in to the stereotypes of liberals that are hawked on populist channels.
but you are ignoring the point I made, writing a comment a priori as if this thread doesn't already exist. I am reasonably conservative, and I understand leftists completely.
I was raised from the crib very left wing, full on commie, with socialist/social justice sensibilities. I was woke before you were born (yes, the word is that old). Then I studied classical econ, and watched the fearmongering about conservatives in the media ("Ronald Raygun is going to start a nuclear war!") never come true.
So, without changing any of my heartfelt sensibilites, I instead realized that the free market ("capitalism") actually delivers the things that working class people need: jobs and cheap goods; and that greedy rapacious capitalist employers have no interest in discriminating against anybody: if women truly earn 60 cents on the dollar for equal work, what capitalist wouldn't hire women to more cheaply make more money? but we don't see that happen, so what the left believes has to be wrong: either the capitalists are not driven by greed, or it's not equal work for less money.
so, no, many on the left who are just like I was do not understand the right, and plenty of us who have moved right from the left do understand perfectly well what noble goals that left sensibilities are trying to accomplish.
Long-term Republicans are shocked not because their party suddenly and without warning became a populist vehicle but because the populist wave that fled the Democratic party during the civil rights era finally took over the party instead of just voting in their preferred old-school candidates.