Uniting people along racial lines cuts across many kinds of class and gender identity, but it divides according to race.

Uniting the working class cuts across many racial and gender identity, but it divides according to class.

So I continue to maintain that this just causes divisions in different places.

You might argue that the surface area of the division is smaller (let's imagine these things as three-dimensional), so it is a more parsimonious cut, but I would counter that we should prefer to not have any cut at all, and that you haven't demonstrated that divisions are necessary. (I would also point out that the economic surface area of the division is actually larger, at least in the U.S..)