May 1 is definitely a holiday and most museums will be closed. I am not sure if the Uffizi and Accademia will be making an exception and having a special opening on that day, it is very possible. But if they do that, we won't know until closer to the date.... for now, checking the online booking website, the date is NOT open, therefore it would seem they are both closed on May 1st. They are both usually closed every Monday, that might be why you're wondering if May 2 is also a holiday (it isn't) because they are also not showing that day for booking. But that is because they would normally be closed on Monday. All things considered, it is possible they will make a decision to do special openings on both days, considering it will be a holiday weekend.
The one that is always open on May 1st, on the other hand, is
Palazzo Strozzi and right now they have the special
Donatello exhibition, which I already visited and highly recommend, especially if you love sculpture. Part of the exhibit is also at the Bargello museum, which will be closed on May 1st, but if you go to Palazzo Strozzi, keep your ticket to get a discount at the Bargello if you go on any of the following days. The Bargello is open on May 2nd, which I confirm is NOT a holiday so anything usually open on that day will be open.
As far as the Duomo (cathedral), since it is a Sunday it is closed because of worship and other religious services. But you can still visit the other sites, as well as climb up to the top of the dome from 12.45pm to late afternoon -- check hours here:
https://operaduomofirenze.skiperformance.com/en/store#/en/support/service
and you can buy tickets here:
https://operaduomofirenze.skiperformance.com/en/store#/en/buy
the new passes are set up by the monuments you want to visit and last 3 days, so you can choose when to activate the pass and then go back to visit a different place on different days, if you don't want to do them all at once. The dome, the bell tower, the museum and baptistery will all be open on Sunday (the crypt is also open for a few hours in the early afternoon on Sundays).
Despite most of the other city and state museums being closed, between Palazzo Strozzi and the monuments around the cathedral I believe you'll have enough to choose from on May 1st!
