American society today is, in some ways, more egalitarian than it has every been in our history. We believe that all people should be treated as if they are equal to one another. However, there are some ways in which we are not at all egalitarian.
We Americans are aggressively egalitarian when it comes to social relations. Americans tend to expect others to call them by their first names, even when one of them is much higher in status than the other. We even go so far as to have teens calling adults by their first names and parishoners calling priests by their first names. We believe very much that we should not act as if any person is inherently better than any other.
On the other hand, we are very opposed to egalitarianism if it means that all people should have equal outcomes in life. We, as a society, tend to believe that it is right and even beneficial that some people should be rich and others should be poor. We strongly resist anything that smacks of "socialism," which would try to raise the poor to economic equality with others through government action.
So, we are a very egalitarian society when it comes to social interactions and to things like legal rights. But we do not believe in egalitarianism in economic outcomes.