When Democrats talk about “our Democracy” they mean the rule of the Democratic party. So yes Republicans are a threat to “their” Democracy.
This is a battle between Individualist and Collectivist.
Individualist are Independent, believe in a Constitutional Republic, private property rights, individual Liberty and economic freedom, limited government.
Collectivist will do what they’re told, group think, socialists, communists, and democracy which always leads to tyranny.