Equality is widely accepted because it can mean so many different things to so many people. The core of equality is some sort of universal sense of freedom, justice, or value. Once you accept that all people have some basic moral value, at least until they do something to debase or surrender that moral value, then you have embraced a form of equality - all people being equally entitled to the presumption of moral value.
Although everybody has different skills, preferences, and perspectives, it can still be true that people have some sort of moral equality. Every worldview believes people differ in their abilities, even if such differences are societal rather than innate; how can socialists or communists rail against a bourgeoisie if it has no extra abilities or advantages? So everyone agrees that people are not equal in their condition. That does not negate the principle that people ought to have some basic equal footing in the moral dimension.
I believe you're getting at the more specific issue of whether the economy, the world, or society rewards and punishes people randomly or commensurate with merit. In other words, do the rich and the poor "deserve" to be in their position. Although this is a common battleground over "equality" it does not have to be the only place equality may be found. In fact, even this struggle, presumes an equality of opportunity to use your natural merits; if you have no ability to hone and burnish your merits because of unequal conditions, then the successful people's merits are less rigorously challenged and proven. Without equality of opportunity (the chance for merit to rise), there is no real point to merit.
I will grant that, at its root, equality is usually taken as an a priori value. The alternatives to embracing some form of equality are generally nihilistic ("things happen and then you die") or flatly prejudiced ("good things should happen to you if you belong to my preferred clan"). Even the sense that all people have an equal claim to not be murdered (absent some other factor, like war or crime), is accepting a form of equality.