If you're reading older works by Haidt, keep in mind that at the time the illiberal left had much lesser standing among the left; a classical European liberal believes in liberty, and a contemporary American liberal does too, but views liberty as going beyond individual freedom to individual opportunity, and is willing to intervene when opportunity is being severely curtailed. This is consistent with their high attention to care/harm as well as freedom. Everything I've read in, say, The Righteous Mind seems consistent with this view of liberals. I don't think that he's stated that liberals care about disadvantaged groups specifically, but rather about the disadvantaged. That's what the care/harm axis is about. (As a practical matter, if a group is disadvantaged you often have an effective way to reduce a lot of harm by helping that group. That doesn't mean that the liberal thinks it's important because it's a group, just because there is harm.) If you know differently, please cite something that demonstrates it.

As the illiberal left has grown--which values care/harm but not freedom (I forget whether they score highly on authority or on group loyalty or both)--I think Haidt's language has become more careful.

The problem with the farthest left wing of the left is that it hasn't really got anything "liberal" remaining to it, so it's a dreadful misnomer. It's entirely reasonable for people who are actual liberals, in the derived-from-liberty sense (whether libertarian or a power-aware neoliberal who advocates for use of government to promote opportunity and restrain cruelty), to refuse to give up the liberty-affirming meaning of the word.

Stalin was on the left. But he was not even remotely a liberal.