Believe me this happens!
On recent trips to Italy, there was a strike at the Florence state run museums until 11:30 one morning. (The same morning, the Museum of the History of Science in Florence was closed for 2 hours due to a problem with the electricity.) Pompeii was on strike until 10:30on one day when we visited. Another time, the Circumvesuviana Train line was on strike. Once, the Galleria Borghese (the museum workers) was on strike for an entire day.
Almost always, the site knows there will be a strike and can advise you in advance. There's a sort of joke in Italy that the best organized things in Italy are the strikes!
If the museum or site allows or requires reservations, be sure to keep the reservation number with you so you can rebook.
Here's a helpful official site on most of the museums in Italy with telephone numbers, including the telephone numbers for reservations.
Museum Information

