What ordinary people think and do is another question. The Ku Klux Klan had millions of adherents. Women did not get to vote until the 20th century. We are left to treat them as fairly empty rhetoric. People, to be sure, tend to SAY they believe in equality.
Some people actually do.
Others think some kinds of equality are fine, and others are not. The same for liberty and justice. I for one prefer to avoid. They had not learned how to rank-order the values. I frankly find this explanation rather flat and unsatisfying.