In contemporary America, we also have people who are — and I am inventing this word here — illegitimists: They believe that the president of the United States is illegitimately elected, or that the country is ruled by a cabal that is in turn controlled by some other sinister force or forces.(She is careful to note that her intent is to be agnostic with respect to political persuasion, by noting that this also described Marxists in an earlier era. Not everyone buys this attempt.)
Just as a word, illegitimist is not unknown. It has no dictionary entry in standard dictionaries (at least, as per Dictionary.com and Vocabulary.com). Even the mighty OED does not have a specific entry for this term. However, there is a precedent or two:
But these are slightly different meanings, I deduce; these refer to people who are illegitimate, as opposed to people who question the legitimacy of something.
This seems like a handy term to me. It covers more ground than various specific manifestations of illegitimism (birthers are her poster child). It gets at a kind of core belief system that's independent of the specifics of why the illegitimist thinks the government is illegitimate, and even which government (or other authority) is being thusly considered.
One could imagine the term being used outside a political context, I suppose. You might use some term and point at the American Heritage Dictionary as your authority, and I could be an illegitimist about that authority. Or we could use the term to debate someone's religious beliefs and the sources thereof; or, if the term really dug in, we could use it to refer to anyone who questions any claim made by an appeal to authority. That seems unlikely, but you never know. Still, the term has to start somewhere. Let's see how it goes.