Of course, May 1 should be an anarcho-syndicalist commemoration, not a Communist or socialist commemoration. After all it was the Haymarket Affair (variously called Haymarket Riot, Haymarket Massacre) that took place in Chicago on May 1, 1886, that is the basis for it, and the labor agitators whose strike turned violent that day when a bomb was thrown at police were not Communists or socialists, but anarcho-syndicalists.
Quite frankly, I want the anarcho-syndicalist Left back. They were perhaps even more suspicious of state power than are libertarians or a lot of us in the pre-Trump Right. I think we could get more done in this country if our opponents were not enthusiastic for the state to intrude into every aspect of life with the possible exception of the boudoir -- they'd be easier to come to compromises with than the current lot, including a reasonable compromise between their favored mode of economic organization (syndicalism, worker ownership in the context of a private market economy) and capitalism.
If Chicago wanted to actually commemorate the Haymarket Affair on May 1, and teach students they were anarcho-syndicalists, not socialists or Communists, I think I'd be all for it.