I do not think that the 3-axes model performs as well as usual at interpreting the post-Brexit feelings. But here is a try.

Let us treat the vote as an anti-immigrant backlash. That might not be correct, by the way. The journalists who are offering that interpretation are the ones who are shocked and appalled by the vote. But suppose it is a major factor.

The oppressor-oppressed view would have to treat the immigrants as the most oppressed group. So, even though working-class natives were traditionally treated as oppressed, you would expect the progressive defense of “remain” to emphasize the plight of the immigrants. I am not really seeing much of that. Instead, I get the sense that there is instead more of an emotional attachment to the project of a united Europe, along with some snobbery toward working-class provincials. I understand how the united Europe fits in with Progressive beliefs, but it does not line up with the oppressor-oppressed axis.

The civilization-barbarism view is that immigration has to be restricted in order to protect British civilization. That would be the language in which conservatives would express support for “leave.” I think we more or less see that.

Finally the freedom-coercion axis says that restrictions on immigration are an especially cruel form of coercion. So it argues for “remain.” And I think that there are some libertarians who express that point of view. But for others, the salient issue is not immigration but instead the Brussels bureaucracy. Regardless of how they come out on net, libertarians do use the language of freedom-coercion in articulating their position.

So on a generous reading, we can say that the three-axes model gets two out of three right.