Someone asked this question, and it's a messy topic. This will be largely an opinion piece by the author. This may be difficult to follow, but there is a train of thought to it.
It doesn't help that the words "liberal" and "conservative" mean something different for each person. I'll typically stick to "to conserve" (hesitant to change / cautious about progressing in a direction) for "conservative", and "liberty-valuing / those wishing to maximize freedoms" as "liberals".
I don't believe there's any real contradiction in being a "liberal conservative". It just means you're maximizing freedoms... cautiously. I'd argue that the opposite of "conservative" is "progressive" and the opposite of "liberal" is "totalitarian".
So barring any synchronization of terms with those who ask the question, that's what I'll have to work with, for definitions.
As a "flaming liberal", personally, I don't see anything intrinsically wrong with conservatism. In fact, I see science as being very conservative. It's very hesitant to change, and is cautious about changing its mind about things, and carefully considering the consequences of decisions, and will throw in a few extra tests just to be sure. Sound familiar?
... and that's good for science, as long as the consensus will eventually change with the evidence-based hypothesis-testing.
I listened to a self-described conservative explain their stance on allowing gay marriage. In short, they are/were concerned about the effects and consequences to society... particularly the unknown ones. By itself, that mode of thought is fine. The problem is... they're wrong... whether we're talking about basic facts, logical fallacies, or double-standards.
It's been particularly frustrating. It's fine to be cautious... but when the the topic has already been well-studied, and the same mind-numbingly bad arguments have been incontrovertably shot down over and over, what we're left with is a stubborn conservative dragging his/her feet while peoples' lives are on hold - marriage rights to those who they want to marry - that include a truck-full of automatic additional rights, like custody rights, power of attorney, visitation rights, etc. Lives ruined because we were delaying too long, due to people trying to retroactively justify a position they came to for non-rational reasons. "Frustrating", to say the least.
That same conservative brought up marijuana laws, stating that it was a fact that marijuana is harmful to you, and that's why they're opposed. The liberal in the conversation pointed out that the same could be said for alcohol, and I'd add fast food. If liberals push to regulate/ban those things, conservatives would be screaming about "big government", but when it comes to their pet topics, then it's just common sense?
That's why this is messy. There's many things we'd agree upon. If we were discussing whether we should allow toddlers to drive, I'd probably take a conservative stance of "uh... no?". I can take liberal or conservative stances about different topics. It's these few key topics, like gay marriage or marijuana laws, that seem to define the overall conversation between "conservative" and "liberal". Those topics in particular bubble up into a fury on a national or global level.
So why are atheists in particular mostly "liberal" (in the sense of more an identity)?
For something like gay marriage, there's also a slew of religious "magic man said no" argumentation coming from conservatives. Once those are dismissed as not being reality-based, by the atheists, there's little left for arguments.
Once you abandon religious totalitarianism, you can't help but become liberal (for these "liberal"-defining topics)... even if you previously held conservative positions. Beyond that, I'm not sure one could even make that assertion. Even among the "socially liberal", you can find division and different positions on a topic-by-topic basis. You can find "liberals" who want to ban cigarettes, and other "liberals" who want to allow it as a personal freedom... but for some reason, cigarettes aren't a defining topic for liberalism vs. conservatism.
If we're to the point of asking why an atheist identifies as a liberal... I can't even speak to that without interviewing each person individually.
Clear as mud?
Even we as a society attempt to run surveys trying to figure out how many atheists there are, it's difficult to get an accurate representation. The way the question is asked can heavily influence the outcome. Asking "Do you believe in a god?" is very different than "Do you believe in some kind of higher power?" ... which is actually sometimes asked. Sometimes, people choose their childhood identified religion over their current status, because they didn't see "atheist" at the bottom of the survey[1].
So asking about something even more nebulous than "atheist"? Good luck!