Assuming that the party of the "Democrats" is the "Democrat Party" is a completely understandable mistake to make (doubly so if you're not from the US). Even if you have seen the correct name, it's easy to overlook given that our brains do not scan every letter in a word

And calling it a "right-wing extremist goal" is bizarre. As far as insulting names for political parties go, it's only extreme in being extremely mild. Is colloquially calling the British Conservative and Unionist Party "The Tory Party" also heinous?

I'm familiar with your point, but ignoring the rest of their commentary and assuming they're taking tea with Greg Gutfeld doesn't help anyone either. It's possible to use a term without knowing its dogwhistle side, and it's possible to be critical of the democratic party without being Trumpian.

You know, I think you might be onto something here. Surely this cannot just be a shorting of "campaign staff of the drmocrats" and "campaign staff of the republicans" that just looks a little weird before you think about it grammatically. No, there's clearly a multimillion dollar right-wing extremist conspiracy afoot to affect a slight change in noun phrases that will have zero impact on any policy or office.

Edit: And my typo of "democrats" as "drmocrats" clearly reveals I'm in on the vicious plot of persecution via zero impact phraseology! Probably getting a check straight from the Kochs, even.