In the United States, May Day isn't really a holiday at all. All we know about it is when people with roots from Germanic countries celebrate the return of summer with children dancing around the ribboned May Pole. We also know it as a day of marches for left-wing or worker political parties promoting their agendas for various worker's rights, similar to how workers in many countries treat May Day.
In Italy, the 1st of May is called Festa dei Lavoratori (Workers' Day), similar to American's Memorial Day or Labor Day. While there might still be workers marching and holding protests depending on which way the the political and economic wind is blowing, for most workaday furbo Italians, it's simply a day off from work and a long weekend to go to the beach, attend one of the many rock concerts, have a barbecue or rent a holiday cabin in the mountains. After all, it's a lot of work to organize and protest on hot city streets, isn't it? Easier to just go to the beach and throw some steaks on the grill.
Most museums are closed as well as many other shops for the entire holiday weekend. This is perhaps not the best weekend to visit major tourist destinations in Italy simply because this is one of the holiday weekends where Italians do the tourist thing... just the way Americans might visit tourist sites in the States during Memorial Day or Labor Day weekends.
Still, in some parts of Italy (southern Marche, for example) a red flag is placed at the top of a poplar tree as a Socialist party symbol. If you're overly anti-communist, don't get paranoid... Italian socialists--and communists--mix well with other Italians and tourists alike. You might meet them later on during the weekend at the beach...
Have a great May Day!