"Equality" is impossible in any society, because no one can agree on the definition when there are so many variables at play. It might be something to shoot for, but since some people don't even care about it, the question is moot.
Equality of outcomes is antithetical to capitalism, however equality of opportunity is very well aligned with the premises of capitalism insofar as it enables society to make the most efficient use of human capital.
Trying to create an equal outcome isn't desirable. It is more important to have a system built upon creating opportunity, and to achieve this individuals must be able to accumulate and invest wealth; otherwise the value of human interaction is set arbitrarily.
This depends entirely on your definition of equality. If you believe that equality means that everyone is treated the same and treated fairly, then it is fair that one man can make more money than another if he works harder.