I mean I'd probably change my answer depending on the phrasing of the question here.

If you mean like, classical liberalism, which includes both laissez-faire capitalism and interventionism, you'd probably find quite a lot of conservatives at this point who would define their economic ideology (if they even have any) as belonging to that kind of realm of thought, at least with laissez-faire. That shit's pretty old, we've been through like multiple cycles of that, both globally, and domestically in america, and calling for a regression to a period when your specific breed of liberalism was in place is pretty possible. Which would be kind of lumped under conservative thought, despite the window dressing of like, wanting to just kind of, hedge your bets, maintain the status quo, and "conserve" things, and even the branding of "this is the way things really are, so we need to conserve the real reality", it's mostly actively regressive horseshit.

So, that's to say, you could both be a liberal and a conservative at the same time, if you're going based on the like, actual political definitions of things. I get the sense you're more trying to use the term "liberal" to mean "progressive", or probably more accurately "socially progressive". If you want a reason why I'm making this kind of stupid semantic distinction, it's because I think it's important to distinguish liberalism, and neoliberalism, right, which refer to economic freedom, from other more actually socially progressive ideologies. I'll get to that later. In any case, it's pretty much part of the intrinsic nature of the ideology that, being okay with gay people, at the least, is going to be more chill than not wanting gay people to exist. The same for trans people, the homeless, racial minorities, neurodivergent people, whatever.

Socially progressive values are also kind of default, I think, in a vacuum (which hardly anything is), whereas nutter conservative ideology is something you have to be more actively radicalized into. If you don't give a shit about gay people, you're probably also fine with them just like, going about life and existing. You might also be fine with their oppression, but you're not actively hindering things, necessarily. You have to be actively radicalized and convinced they're bad, though, in order to call for them to be like, killed, or barred from marriage, or whatever.

You would have to more actively want gay people to have rights, to care about them more in a positive way, and actively oppose their oppression more, in order to like, actually push for things. It's a more active position, basically, to be actually socially progressive, or actually progressive. It necessitates caring. I think despite it just being on the surface more nice as in ideology, which helps prevent people from being like, actively hateful, I think it's probably also sadly the case that a lot of people who would otherwise pretend to be socially progressive don't actually give two shits about what happens or doesn't happen, and are just mindlessly occupying what they see as kind of a default position at the time.

If you go back to like the 2000's, lots of people who are otherwise pretty "progressive" nowadays would've been pretty turbo homophobic and transphobic. That's not really a slight against their character, right, we're all products of our environment, but they're just occupying kind of whatever position they think is acceptable to the mainstream.

Put even more simply, they kind of, understand that one side is right and one is wrong, but since they don't really understand the underlying reasoning behind either side, they're just jumping onto whatever they get better vibes from. That used to be some more reactionary stuff, because we were kind of in both a more apathetic and callous cultural era where "not caring" was seen as cool and offering a better vibe, and we were seen as being kind of in a "post-history", "post-racial" world, where if you were offended by racism, that was your fault, because we ended racism, and now the only real racism is you thinking racism is real, man hits bong. Just sort of like, the idea of racism as existing in a purely cultural state, just as a remnant, a cultural artifact relic which we need to move past culturally, but doesn't affect the "real world" in any way. Those ideologies were kind of appealing to a mostly white mainstream cultural population, who could pretty easily just walk around, and make edgy jokes, and pretend still that everything's gonna be okay because they haven't encountered a housing market crash and the consolidation of all of the wealth in a fraction of the population and a once in a century pandemic partially accelerated by huge misinformation campaigns. Basically, because the mainstream cultural consciousness, mostly controlled by white people, was still insulated from the worst of the worst consequences, and because they were still getting treats.

We still had a white suburban middle class, basically. We still do, but we used to, too.

Now though, people see being socially progressive as having a better vibe. Probably this is because we're on the long end of the economy being shit, and everyone having realized that collectively burning your children's futures in order to further white supremacy isn't a sustainable thing long term and just fucks you over, probably it's also because the internet has made it easier for marginalized voices to occupy more space in the cultural consciousness, whereas before they would've been screened by industry gatekeepers. Probably it's also because conservative nutters collectively lost their fucking minds and kind of went mask off with trump and gamergate shit, partially as a reaction to obama just being like, black, but also those other factors I've named.

Probably it's because the middle class that you used to see in all those 90's movies, like fight club and office space, got automated away, outsourced, or otherwise traded for a bunch of IT and internet developers, which can mostly take their place as part of the managerial class. We go from cubicles in high rises, to open floor plan offices in mid-rises, to work-share rental spaces in low-rises, to work-from-home setups, and the amount of people allowed treats from their overlords narrows in total population because you simply don't need as many. The amount of people who are actively fooled by corporate propaganda and bootstraps mentalities also narrows with the proliferation of the internet and with the lack of people who are now "in" on this middle class lifestyle, so your immediate social group is more likely to have people who you know are chilling but are also struggling a lot financially.

yeah I think that's all I got as far as this one goes.