This is a political question more than an economic one. One way to answer it is to say that inequality is not a big deal as long as the people who are lower on the economic ladder are making absolute (as opposed to relative) progress.
One can argue that absolute income is more important than relative income. If the lower and middle classes are getting more and more money and a higher standard of living, they will not necessarily care if the rich are getting even richer. However, if the rich get richer and the poor and middle classes do not come to be any better off, they may become angry.
Today, this is how things seem to be. Incomes for the middle class have been stagnant for the last few decades. If this continues, the income inequality in our country could be a cause for concern.