“A representative Republic is a type of democracy. Will people look this up?”
That’s way too advanced for the dummies who always chant “We’re not a democracy” when it comes up. It seems nuance is out of their reach.
As to the topic at hand, although we practice democracy in much of what we do, we're not technically a democracy; rather, we're sort of a "controlled democracy", carefully and deliberately designed by the Founders to pull the reins in on mob rule by a simple majority. It is irresponsible -- if not a little foolish -- to dismiss this essential diffence in both meaning and application by dismissing it as a "nuance".
My point here is that those who call attention to the distinction between "democracy" and "representative republic" are not "dummies". Far from it. They are merely demonstrating their superior knowledge of the country's founding and of the wisdom of the Founders.
Cheers!