Loyalty Day, as many have pointed out, is not some weird thing Donald Trump thought up. It is an artifact of the weird things we used to do during the Cold War (and even before–it dates to the Red Scare of the 1920s) when we were scared of communism. To me it is the kind of thing that actually sounds like what an authoritarian regime would have, rather than something a democratic regime would do to criticize an authoritarian one.
(It is also an example of how we in the US do not like to celebrate labor in the collective sense, as May Day has associated with organized labor since the mid-19th century.)
You can compare Loyalty Day proclamations issued by Trump, Obama, and Bush here.