Working for and advocating the establishment of rough equality* is the essential property of progressivism. I call this notion "progressivism" because we are making progress away from the elitist authoritarianism that was the essential character of past political systems — most notably the maximally elitist absolute power of the individual monarch — in favor of more politically egalitarian democracy.
*Dismissing (out-of-hand, for the moment) the Harrison Bergeron almost-straw-man notion that equality entails erasing individual differences.
Under this definition, one cannot be a progressive while being sexist, i.e. holding that women are inferior just by virtue of their gender. In the same sense, one cannot be a progressive while being racist, or a homophobe, or a nationalist**, or holding any other bullshit establishment of inequality. But while eliminating these bullshit distinctions is necessary, it is not sufficient to implement progressivism.
**In the sense of holding that some people are inferior just by virtue of their nationality.
We are still left with the more refractory notion of economic class. Class is not transparently bullshit in the same sense that racism is transparently bullshit. When class was explicitly determined by virtue of heredity, as during feudalism, it was transparently bullshit; The West, however, especially the United States, has to a substantial extent transformed class into a sort of meritocracy. Class by merit is a definite improvement over class by birth (or race, or gender, or sexual orientation, or nationality, etc.) but it's not enough. Class itself, however it is established, is inherently unequal.
First of all, the notion of "meritocracy" is ambiguous and subject to equivocation. There are two definitions of meritocracy. The first is the unobjectionable notion that we should reward people according to their individual merit. The more problematic notion is that we should concentrate power ten-million-fold and give that concentrated power to the "best" among us. To equivocate these two notions entails holding that Bill Gates is ten million times better than an African subsistence farmer. Another way of looking at it is that the United States' 300+ billionaires are worth more than 90-95% of the people of China put together.
Such a notion is patently absurd. (There are those who would argue this sort of meritocracy directly and explicitly, notably Ayn Rand, gleefully contemplating the fall of civilization when a few thousand rich bastards exempt themselves from human society). The notion that one human being could be ten times better than another is barely credible; just a hundred times better is obviously ridiculous. Ten dumpy out-of-shape middle aged white guys like me could beat the NBA MVP in a game of basketball. I'm a damn good computer programmer, but you could take a hundred random people off the street, give them the same sort of training that I had, and they would certainly out-produce me, probably by an order of magnitude. And these examples arein a areas of narrow specialization, where "better" and "worse" can be objectively measured.
Why does Bill Gates have tens of billions of dollars? There's no possible way he could actually personally consume that much wealth, even with the help of his immediate family. There's only one reason to have that much money: To control what gets made and who gets to use it. In short, to gain power. And this sort of economic power is of the same essential character as political power: Whether or not a person gets enough to eat, and has a right to dignity at work is just as important as his liberty, dignity and well-being at home.
Even the most cursory study of history (real history, not fourth-grade civics propaganda) shows that concentrating power is a Bad Idea in general. Power, by its nature, perpetuates itself, and once you give real, concentrated power to an individual, it is he (and it's usually been men) who decides who gets the power when he decides. Once the people create a King and become his subjects, the only way they themselves can decide who becomes the next King is violent, destructive, wasteful rebellion. Even if we luck out and make a saint our King, that's fine for today, but what about tomorrow?
We have learned that it's best not to concentrate political power too narrowly, and when we do concentrate political power at all, we must create elaborate democratic institutions to make those who exercise that concentrated power responsible to an informed, realistic electorate.
We don't know that democracy is the correct solution to the concentration of political power, but we do know that every society that has concentrated political power without democracy has eventually oppressed the population to the extent that they had no choice but to starve to death, rise up in rebellion, or degenerate into anarchy and Mafia rule. Yes, Stalin turned the most backward country on the Eurasian continent into a global superpower in a generation, but two generations later the Communist party ran Russia into the ground, perpetuating the cycle of totalitarianism and chaos. While the jury is not yet in on China, I expect the same thing to happen; the cycle of totalitarianism and chaos is readily apparent in Chinese history.
It is ridiculous that any person could be ten million times better than any other person — great economic wealth is not earned by inherent individual merit — therefore such wealth must be socially constructed: it is granted by the people at large. Since great wealth cannot be deserved by individual merit, we must evaluate schemes that grant great wealth to individuals not on the scheme's "intrinsic" merit, but on its consequences. And the consequences of concentrating power have invariably been bad for everyone, even those who actually held the concentrated power (just ask Czar Nicolas or Marie Antoinette).
Thus we can conclude that the only progressive position on economics is to distribute wealth many orders of magnitude more equally than it is presently distributed. Furthermore, where wealth is concentrated, it must be under the power of democratic political institutions. In short, progressivism entails socialism.
Nothing changes, nothing stays the same. The only choices are progressivism (more equality), regressivism (less equality) or passivity. The "true" conservative, someone who wants things to stay exactly the same is deluded or dishonest. You are either progressive, regressive, or an instrument of progressives or regressives.