Democratics versus Democrat

Members of The Democratic Party don't mind being called Democrats.  But consistency would require that Democrats belong to the Democrat Party.  But they take extreme umbrage when Republicans call them the Democrat Party. But the english language probably has a rule about this somewhere.   Now I don't know what the rule is.  I made Cs in english.  I'm just trying to figure out a way to be consistent when I refer to Democrats(ics), Republicans and Libertarians.  I mean Republicans are not called Repubs.  Libertarians are not called Libertars.

Members of the Libertarian Party are called Libertarians.  Members of the Republican Party are called Republicans.  Members of the Green Party are called, we'll they're called a lot of things but for this excercise they are call Greens.  But members of The Democratic Party want to be called Democrats.  The Republicans, trying to be consistent typically refer to Democrats as being members of The Democrat Party.  This pisses off Democrats who prefer the more democratic sounding Democratic Party.  Ya'll following this nonsense?

So I think we should start referring to Democrats as Democratics.  That way members of the Republican Party are Republicans, members of the Libertarian Party are Libertarians and members of the Democratic Party are Democratics.  Oh, and members of the Green Party should be refered to as Communists.