What might we expect to be closed on May 1st in Florence?
I do not know, but the major sites each have websites. I would go to those and check for myself. Closing days can vary from year to year, so I would not rely totally on information in guidebooks or on other travelers' reports.
We were in Florence on May 1 two years ago and it seemed ALL the museums were closed, BUT our hotel owner told us that the Boboli Gardens were not only open but free -- lovely walk!