It's up the Austrians, to be sure. But the rest of us get to say they are wrong in this.
t is impossible to reasonably deny the holocaust just as it is to deny WWII. To do so one must either be engaged in a publicity stunt or suffering from mental illness. In each case they should be ignored but the media won't.
However, the right to free speech guaranteed in the first amendment is not unabridged. We can be arrested for inciting a riot, yelling fire in a crowded theater, lying to a police officer, lying under oath in court, etc.
Also, as noted, this arrest happened in Austria where they are a little goosey from recent history.