We do not have complete equality in the United States, when it comes to civil rights.
For one thing, there are groups that claim civil rights but do not have them. The most prominent of these groups today is homosexuals. Gay people do not have the right to marry, among other rights, in most states. Thus, they do not have complete equality.
Even when it comes to groups that are more protected, there is not complete equality under the law. Women, for example, are prohibited from being in combat positions in the military, regardless of their physical abilities or the demands of the particular military occupation. African Americans nominally have all the same rights that other Americans have, but there are still issues of equal opportunity because many African Americans are poor and poor people (for example) tend to have less access to decent public schools.
In all of these ways and many more, we do not have complete equality in the United States.