Whether or to what degree Plato's Republic is a utopian work depends on what one means by “utopia,” a word with a notoriously wide range of meanings. I shall simply stipulate that by “utopia” I mean a description of an imagined society put forward by its author as better than any existing society, past or present. The limiting case (relevant to the Republic) is the portrayal not just of a better society but of the best society. I call a “mere utopia” a description of an ideal society meant or recognized by its author to be an impossible society - a society in some sense better than any historical society, but which could never actually exist.
Socrates calls his ideal city “Callipolis.” Did Plato think Callipolis was realizable? Did he really believe that the city he portrays in the Republic is the best human society? As with so much else in Plato, scholars disagree. One mainstream interpretation, which fits most easily the surface of the text and which I share, is that Plato intends the society described in the Republic to be a utopia that is not a mere utopia. Socrates paints a picture in words of the best human society, one difficult but not impossible to realize.
Compared with classical Athens, or indeed with any society existing today, the conditions in Callipolis are extraordinary. Communism of property, abolition of the family, tight control of every aspect of life by the philosophical ruling class, maximal “unity” of thought and feeling among the citizens – features such as these have led critics from Aristotle onward to criticize Callipolis as so contrary to human nature as to be both impossible and undesirable.