I'm not at all convinced that 'intellectual' liberals understand 'intellectual' conservatives, speaking as someone educated in the American higher education system.
My stance is pretty firmly that neither side understands the other at all, whether we're talking about intellectuals or otherwise.
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.
>My stance is pretty firmly that neither side understands the other at all
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.