This is not the best term to use to define the social order in the United States right after the American Revolution.
Republicanism generally refers to a system where the government is kept somewhat separate from the people. The people do still play a major role in government, but they have less control over it than they would in a democracy. (Please note that the difference between a republic and a democracy is extremely vague and fuzzy.) This would be a better term to use to describe the social order after the Constitution was ratified. Right after the Revolution, America was more democratic under the Articles of Confederation. The power was with the states and the states generally had very democratic constitutions.