From the graph (above) linked by the top comment in your [2], I'm wondering whether this demonstrates more anti-conservative bias than liberal bias, or whether the alternative meanings of conventionally conservative versus conventionally liberal words dictate the frequency of a flag.

For instance, "Republican" means a variety of things around the world, but "Democrat" is far more likely to indicate the US Democrat party (which is frequently misstated as the "Democratic party"), or a national Democrat party in general. People would tend to write "I'm a democrat" to assign their membership to the party, whereas they'd say "I'm democratic" to assign their leanings toward the system. But "I'm a republican" means both.