'Denying' the Holocaust is theoretically and formally legal in the United States, but for practical purposes it is not because Big Tech suppresses it. It's unclear what a president could even to do to suppress Holocaust Revisionists even more if he wanted to.
As for U.S. federal-government-sponsored efforts against Holocaust Revisionism and the prospects for 2021 to 2024, I'd make these general comments, which can be summarized in a single three-word question:
Does "Biden" matter?
The true forces that function as "the regime" in the United States, a "regime" that has still-considerable influence over its cultural-political quasi-satellites of the old NATO bloc and beyond, is (at the risk of saying something obvious) diffuse. It is not limited to the person of a president or even the entire sum whole of all the elected officials. Any definition of what "the regime" is today
must definitely and unambiguously now include what we call Big Tech, among other forces. The press has always been influential, but Big Tech has power in a way "the press" of decades past never did and never could in a reasonably open society. This power is, for any practical purpose, political. (Big Tech all colluding together on information flow and creating a 'party line' backed by massive propaganda is, ironically, something quite comparable to the Goebbels machine at the height of the peacetime Nazi regime.)
What these unelected actors want to do, are doing, or will do, on something like Holocaust Denial is theoretically independent of what Biden or the faces he brings in do, or want to do, or will do. But really it all exists within the same consensus. It all forms an amorphous whole. "What will Biden do" may be the wrong question, with the better question being "What will Big Tech do?"
As for the formal government consisting of elected officials and their staffs: The all-but-unremarked-upon scaling-up of the State Department's Global Anti-Semitism Commissar position under Trump is revealing. It shows how little a changing of the guard at the top can mean for the mechanics of how things work. I mean, Trump ran on, and continued to regularly rhetorically oppose, any kind of open-ended global commitments and interventions of dubious benefit to actual Americans. An endless war against anti-Semitism and Holocaust Denial (as if the two are identical) is the kind of strange foreign commitment Trump often railed against. But, with no fanfare, Trump signed a bill into law last week that vastly increased:
See Jan. 2021 update in thread "
The US State Dept.'s "Office to Monitor and Combat anti-Semitism" and state-backed Holocaust Enforcement":
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