While the literal term isn't used the way the parent describes I believe that their comment is trying to communicate "While only half of Americans describe themselves as Democrats, most Americans would say they're "an advocate or supporter of democracy" (the definition of a democrat).

Right, but when arguing semantics, then semantics matters. "democrat" as in "someone who advocates democracy" simply isn't in common usage here.

Likewise, if I said I donated to BLM, odds are good I am talking about the fund by that name, not an abstract concept of a movement that random people ephemerally belong to.

Thank you for clarifying my post. That is indeed what what I meant.

Perhaps they meant: Americans will all claim to be democratic*