This pops up every now and then and is complete bullshit. A republic is a system of government with a parliament and an elected head of state. Being a republic and being a democracy are completely unrelated. There are republics that are oligarchies, dictatorships, or democracies. Similarly, there are monarchies that are oligarchies, dictatorships, or democracies.

You can discuss about legitimacy and the fact that the US is a federation of states instead of a government of citizens, but “it’s a republic not a democracy” is stupid. Using it as a way of justifying blatant undemocratic aspects of the way the US work is doubly so.