Oppressed minorities care about inequality, women care about inequality, the differently disabled care about inequality, greens care about inequality of access to ecological resources, and so on. Identity politics and new social movements are in small or large part aiming to reduce inequality. Problem is that this tends to suppress class inequality. I mean, identity politics demands for more equality for ascriptive and quasi-ascriptive groups. This is a step forward in so far as these demands seek to equalize identity groups within the working class (roughly similar to the 1920s, when Pole, Slovak, Serb, Italian, and other ethnic groups in heavy industry got to know one another, did a lot of the spade work to make possible culturally and politically the industrial unions of the 1930s; see also the 1932 election, when working class women voted in large numbers for the first time, they voted for FDR, as the best hope to tackle the problem of equality between women and men, and also to some unknown degree between capital and labor). Identity politics is a step backward to the degree that class politics gets repressed (for example, in Silicon Valley, when women workers demand company child care facilities because they are women and mothers, instead of demanding more wages because they are workers).
The unions say they are still for less inequality, not just between workers pay and CEOs' tens of millions annually, but in society as a whole. But the unions used to legitimate these demands or desires in terms of social ethics or the preconditions for stable community or something important needed for social integration a la Durkheim. Today they are much ore likely to develop economic arguments re: systemic needs and functions. Like the minimum wage increase is good because the system needs people to spend more money, i.e. it's good for aggregate demand, rather than because people really need more money to spend. Unions typically defend the idea that minimum wages and such are good for "economic efficiency" on the grounds tat they don't reduce employment hence don't "misallocate resources." The banner of equality today is frayed (like everything else) by neo-liberal ideology, by capital's monopoly on legitimate language one can use in "normal" political discourse.
I think red greens/green reds especially need to think through the whole issue of equality/inequality because along with "sustainability," "equality" will likely be the second Big word in the green left/left green future (if we have any at all). The significance being that sustainability and equality are dialectically related in a number of ways, e.g., equality of access to land and ecological resources in the South is a precondition for sustainability if farming, etc.
I do believe that it's a long way from Gini Coefficients to the social psychology of inequality. In the last chapter ("Personality Crisis") of my book, Meaning and Crisis, wildly ignored this side of Barcelona and Rome, I try to show how and why many or most people have ambivalent feelings about inequality, conflicted feelings. On the one hand, deprivation fears (I want more) and guilt fears (I want to do more and will take less). A perfectly functional dualism given that consumerism (I want more) is the other side of surplus value production (I want to work harder and smarter than any of you guys). And so on.