This topic might divulge into Democratic Socialism not Democratic Republicanism.
Socialism (and Marxism, Communism, etc.) was originally supported by secular Jєωs, but ʝʊdɛօMasonry brought about today's Republics from the destroyed monarchies of Christendom.
America is a Constitutional Democratic Republic not a Democracy.
But modern "Democracy" (in contrast to the original pure Democracy of ancient pagan Athens in Greece) was most likely a product of humanism and the Rennaissance, not to mention Masons like John Locke.
EDIT
I guess I'm trying to say "Democracy" can be used in many systems and the word by itself is used very vaguely.