Conservatives are much better, these days, than are progressives (I hesitate to call them "liberals" for reasons I will get to in a moment), with accepting the viewpoint diversity that is expressed by people who are on their side.

However, conservatives are much worse, these days, in generating a set of diverse viewpoints and then narrowing down these viewpoints on the basis of evidence.

This isn't because conservatives are bad at sharing facts or don't think facts are important, but because the quality control is extremely low and--consistent with the general importance conservatives attach to authority--the willingness to accept authoritative-sounding statements from someone "speaks plainly" or otherwise has high identity-group-cred is very high.

So you end up with preposterously enormous fractions of conservatives believing that the 2020 election was stolen from Trump.

Practically, most conservatives are, unfortunately, rather bad at making any use of viewpoint diversity. The more-widely-believed views aren't believed more widely because they have better evidence, because confidently-stated rubbish is allowed to stand in for actual evidence far too often. But a lot of conservatives reveal that they don't actually want to have to be subjected to diversity because far too many of them support bans on material contrary to their ideology under the guise of it being morally corrupting. (Sans evidence that it actually is. Well, sans any evidence that isn't just loudly repeated rubbish.) In that way they are illiberal.

Most progressives are, unfortunately, rather bad at even having viewpoint diversity these days because if you have a different view, it's probably because you're a fascist, and if you're making arguments, it's probably because you're using the techniques of whiteness to extend your oppression. Or something. They're also illiberal, because they don't want you using things like "asking questions" to cover for your inflicting pain upon the oppressed. Or something like that.

Actual liberals like viewpoint diversity, and take proper advantage of it. This is really as core to the (classical) liberal outlook as anything can be.