All democracies have minimum criteria for participating: for voting, or for standing for office. Recent RL events have reminded us that officeholders may be impeached and barred from ever holding office again if they engage in high crimes and misdemeanors, such as insurrection.
The Constitution broadly favors freedom, but it is not a suicide pact.
Certainly an avowed desire to end democracy is as good a reason to exclude Nazis from participation in it.