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I suppose there is no choice other than having to waste one's time on debunking other people's lies and misrepresentations, because one can't just ignore them, thus "giving them credence". Cue Irving's London lawsuit against Jewish US academic Deborah Lipstadt, which she won on all counts: Irving IS a deliberate falsifier of history, end of. Pity the Obamas can't sue for libel for every single instance of deliberate misrepresentation.
On one level it's a Sisyphean task because we are talking prejudice here, and prejudice always works the same way, no matter whom it is directed against - Jews, Muslims, Catholics, Protestants, black people, white people, yellow people, brown people, whomever. A prejudiced person will frantically attribute to OTHER PEOPLE what she/he most hates im THEMSELVES ("denial and projective identification" in psychoanalytical parlance). This is why there is an unending stream of smears every time the prejudiced person thinks of their hate object, and they don't mind what they say either, however off-the-wall it may be, because it relieves the prejudiced person's inner tensions for that one moment, and flummoxes the recipient with its crass absurdity and unreason. It's actually INTENDED to create that "shock and awe" moment in THE OTHER, whoever he/she may be, because "joyful cruelty" (New York psychoanalyst Otto Kernberg) is highly addictive for prejudiced people, as is the need/greed for self-congratulation/self-adoration.
Of course the prejudiced person is also the last to notice any of that in THEMSELVES. But the debunking still has to be done: Thank you.
In the late 1920s and early 1930s, Joseph Goebbels - prototype of unrepentant and deliberate liars and smearers - persisted in calling the deputy police chief of Berlin, a lawyer who happened to be Jewish, "Isidor". (Look up "Dr. Bernhard Weiss"). I'm afraid it worked at the time, for the same reason that crypto-racist smears work on the Obamas: There is just such an endless flood... but it still has to be resisted.