May Day has been around a lot longer than Communism. It has been celebrated in all over the world, in countries before they became Communist, and remains celebrated today after those same countries rejected Communism. And it is celebrated in countries that never were Communist. Even pre-Castro Cuba celebrated El Primero de Mayo, Dia de los Trabajadores.

The fact the Communists celebrated it means nothing, they celebrated New Year's Day, too, that doesn't mean they co-opted it.. As far as I know, only the USA has felt the need to embarrass itself by abandoning an accepted international holiday and create its own, to celebrate the exact same thing. I don't have any doubt it was the result of a desire to conflate Socialists and trade union activists with Communists., which is precisely what that website is trying to do.

I suspect at least two other readers made the same observation:

Tanya says:
"Labor deserves its own day and the fact a day used to honor it was abused by communists doesn’t mean the day itself should have its purpose changed. The realistic result of making a day honoring labor into a day honoring victims of communists is to harm labor, since it will be tarred with the same brush in various ways. "

gray says:
"At best the proposal is patronising and offensive to the Labour Movement. That the USSR tried to co-opt the day doesn’t diminish the origin of the day or the worthiness of its observation."

"Solidarity" was a Polish trade Union, and its leader, Lech Walesa, was not just a trade union organizer, he was a shipyard electrician. He was a worker.