I wouldn’t worry about that. Most libs don’t read theory and the ones who do openly admit to one label or another. Classical liberal, neoliberal, etc. Conservative liberals like to be specific about which one they are. ‘Progressive’ liberals are sometimes specific – that’s mostly the politicians, the policymakers, etc.

The average voter, including the academic liberal, tends to be general and to use the word in this fluffy way that somehow means progress but without stopping global exploitation. These are the ones who can themselves liberal and think they know what it means but completely fail to understand the implications. They’re at most danger of cognitive dissonance because there’s no way to square the contradictions. That said, even ‘conservative’ liberals tend to dismiss accusations of their racism; there’s almost always a ‘but …’.

Neither the classical liberal nor the neoliberal nor the social democratic Keynesiam liberal care much about the out group, though. It’s all there in the main works. They just don’t like being called out on it. But you try to explain how all those cheap items end up in the western supermarket and reverb the most progressive liberal will start hand-winging.