> The correct adjective to use when referring to its members is Democratic.
The correct noun to use to refer to the members of the Democratic Party is Democrats. It's plastered all over their website and the host name of their site.
> A faction who feels justified in maintaining existing anti-democratic structures in order to retain power while not being able to win the popular vote.
Since when was winning the popular vote ever the criteria to "retain power" on the federal level? The Electoral College ensures the popular vote is not directly correlated with winning the presidency. The Senate was also designed to give additional power to states which were not as populous as other states.
> That same faction wants to divorce the concept of democracy itself from the Democratic Party.
How does calling the Democratic Party the "Democrat Party" do that? A democrat is someone who supports democracy. There is no divorcing of the concept of democracy when using "Democrat Party" in place of Democratic Party.
> Again, I link you to the wikipedia page on the subject
I'm sorry I cannot take that Wikipedia article seriously.
Grammar does not even come into play. Nouns are commonly used attributively: water pipe, city streets, television station, Democrat party.
Democrat rhyming with autocrat, plutocrat, and bureaucrat? Well democratic rhymes with autocratic, plutocratic, and bureaucratic so it is pointless to argue that.
As for using "Democrat Party" for the emphasis on "rat", I guess Democrats should stop denigrating themselves and call themselves something other than Democrats.
> This rhetorical war didn't happen by accident.
And again, Democrats is the Democratic Party's primary identity to the average person. The only group which started this "rhetorical war" of using "Democrat Party" are the Democrats by way of using Democrats as their primary means of identification.
Democratic Party's website:
https://democrats.org/
Joe Biden - "I ran as a proud Democrat."
https://joebiden.com/presidency-for-all-americans/
Until Democrats change their own habits and start using Democratic <whatever> in place of Democrats, Democrat is how the average person will identify the Democratic Party.
> Lastly, you should call people like they like to be called.
I did not see anyone addressing you specifically as Democrat. If you are a member of the Democratic Party, I suggest you take it up with them. They identify their members as Democrats.