(Note: This blog post started as an answer I wrote on Quora.)
As I’ve grown more experienced and looked out over the world, I’ve noticed that self-identified liberals and self-identified conservatives love to attack each other for “virtue signaling,” even though it’s far from unique to one side of the political spectrum. They often end up talking past each other, though, because they do it in different ways, against different targets.
One key difference between the left and the right is often the way they feel about hierarchy. Political conservatives tend (with some exceptions, of course) to lean toward vertical hierarchies; political liberals, toward flat egalitarian social structures.
This isn’t just an American thing. Peer-reviewed, published studies have observed this difference across different societies.    There appears to be a structural, neurological basis for this division. 
So how does this play out in virtue signaling?
The simple answer is: While both liberals and conservatives frequently virtue-signal by denouncing external threats or perceived threats—members of the out-group—liberals are far more likely to turn on their own, virtue-signaling by attacking members of the in-group seen as violating the norms and standards of the in-group.
That might seem contradictory at first. If conservatives value hierarchy, and with it conformity, doesn’t that mean conservatives would be likely to turn on people perceived to be insufficiently adhering to the group’s thinking?
And the answer is no.
When you are part of a hierarchy and have strongly hierarchical views, it seems like a natural consequence of that hierarchical thinking is a set of double standards for those at the bottom of the hierarchy vs those at the top. This is how conservatives can claim to support “family values” while worshipping—sometimes literally—a twice-divorced serial adulterer who’s had five children from three different women.
Adherence to the hierarchy itself is what’s important. The people at the top aren’t subject to the rules.
Liberals don’t accept this. Liberals are biased toward egalitarianism; the same rules apply to everybody.
On the one hand, that makes liberals far less likely to overlook transgressions on the part of those at the top. Al Franken was urged to resign when a photo showing him pretending to grope a woman (without touching her) started circulating; on the other side, Matt Gaetz is the subject of a criminal investigation for statutory rape, pandering of a minor, sex trafficking of minors, and obstruction of justice—an investigation that has already resulted in the criminal conviction of a co-conspirator—and conservatives are like “eh, whatever.”
This difference in reaction comes directly from differences in attitude toward hierarchy and egalitarianism.
What this means is that liberals and conservatives both virtue signal, and in many of the same ways, but when they, for example, crank up the Twitter rage machine, conservatives are more likely to target members of out-groups, whereas liberals are much more likely than conservatives to eat their own.
Which is not to say that conservatives never target their own or liberals never target the out-group, of course. One of the biggest modern examples in American history of cancel culture was the conservative rage at the Dixie Chicks, which resulted in employees of radio stations that played their music being stalked and receiving death threats, and venues that hosted Dixie Chicks concerts getting bomb threats.
But the Dixie Chicks committed a crime against hierarchy; they questioned George W. Bush’s rationale for war in Iraq.
This is a big part of the disconnect between liberals and conservatives about cancel culture and free speech. Conservatives will cry about “Liberal cancel culture! Liberals don’t care about free speech!” But when liberals are like “wait, isn’t that what you did with the Dixie Chicks?” conservatives will say “no,” leaving liberals thinking “what a lying pack of hypocrites.” But from the conservative perspective, they aren’t lying and aren’t hypocrites. The Dixie Chicks were attacked for undermining the hierarchy, not for speech. The fact that speech was the tool they used to undermine the hierarchy is an irrelevant detail.
Liberals, on the other hand, turn their virtue-signaling on their own, often for “offenses” that seem inexplicably petty and stupid to conservatives.
This happens to an extraordinary degree in small liberal subcommunities—often, the smaller the subcommunity, the more vicious the virtue-signalling and infighting. I’m reminded of the Henry Kissenger quote, “The reason that university politics is so vicious is because stakes are so small.”
A real-life example:
Some years ago, a woman complained on Tumblr that she didn’t like polyamorous people because polyamorous people would talk about being “poly” on Tumblr posts, and it made it harder for her to search Tumblr with “poly” to find Polynesian Tumblr users.
Now, this was one person on one social media platform, not Polynesian people in general.
But the polyamory scene, or parts of it, started to turn—sometimes with incredible viciousness—on polyamorous people who used the word “poly,” demanding that they use “polya” or “polyam” instead.
To polyamorous people, those who use the term “poly” committed a crime against the marginalized.
This, too, is a big part of the disconnect between liberals and conservatives about cancel culture and free speech. Liberals will cry about “Conservative cancel culture! Conservatives don’t care about free speech!” But when conservatives are like “wait, isn’t that what you do when you police language around minority groups?” liberals will say “no,” leaving conservatives thinking “what a lying pack of hypocrites.” But from the liberal perspective, they aren’t lying and aren’t hypocrites. The people using the word “poly” were attacked for undermining a historically disenfranchised group, not for speech. The fact that speech was the tool they used to undermine this group is an irrelevant detail.
This kind of policing of the “insufficiently woke” is far more common in liberal than conservative scenes, and it turns easily into virtue signaling when people uninvolved with the original whatever-it-was start to pile on because piling on is an easy, no-cost way to be seen on the side of the righteous. (There’s another pile-on starting up these days about people who use “consensual non-monogamy” vs “ethical non-monogamy” to describe polyamory; the idea is that consent isn’t necessarily ethical, so the people who use “consensual non-monogamy” clearly don’t really care about ethics.)
The pile-on is kind of the definer of virtue signaling. Once it becomes socially acceptable within a certain group to attack a certain person or subset of people, those without any dog in the fight will pile on merely for the admiration of their peers.
Well, also to congratulate themselves for being moralistic too, I suppose, but I gotta say, when you express your virtues only when it’s safe and easy to do so, costs you nothing, and there’s no risk…are they really virtues?
Left and right virtue signaling is generally quite similar:
- It involves attacks on perceived threats to the orthodoxy. In conservative circles, the orthodoxy is likely to be the current hierarchy, or dominant religious or social tradition. In liberal circles, the orthodoxy is likely to focus on perceptions of egalitarianism and power imbalances: men always have more power than women (hence “believe all women”), and so forth.
- It is an easy tool of bullies to use to exert authority and control. Bullies skilled in whipping up outrage can direct that outrage against targets of their choosing by manipulating the values of their social group.
- It is safe, risk-free, and no-cost for those who jump in. Hopping on a bandwagen is pretty much the safest thing you can possibly do; in fact, the person who stands up against bandwagoning is the one who risks more. (Ask anyone who refused to name “Communists” during the McCarthy witch hunts!) The real determinator of your virtue is not what you do when proclaiming your virtue costs you nothing, but what you do when holding to your ideals costs you something.
Where they differ is in the common targets, and of course in the rhetoric used to justify the virtue signaling.
 Conservative and liberal, hierarchical and egalitarian: Social-political uses of the concept of “home” in Greco-Roman antiquity and early Christianity
 Liberal and Conservative Representations of the Good Society: A (Social) Structural Topic Modeling Approach
 Political identity, preference, and persuasion
 A Neurology of the Conservative-Liberal Dimension of Political Ideology
 Political Orientations Are Correlated with Brain Structure in Young Adults