Back up plan if train to Cinque Terre (from Florence)is on strike

Some helpful info to put you at ease: https://www.italiarail.com/strike-information

Strikes are usually announced ahead of time, their duration is known, and
they are commonplace enough that everyone knows what to expect.

There are websites that keep lists of upcoming strikes; I'd start following
them a week or two ahead of your trip.

Also, the different train services (local, regional, national) are operated by
different unions in each country, so just because you hear of a strike
doesn't automatically mean you're impacted.

And sometimes strikes are called off at the last minute.

As noted, you will be accomodated if a strike does occur. I suppose the
best thing you can do is research alternative train schedules as your dates
get closer and have those available.

If the date of the September strike falls on a Sunday, as does the strike occurring this coming weekend on May 4 & 5, there are no guaranteed Regionale ( local) trains that are covered by Trenitalia’s agreement with the rail unions to have Regionale trains run between 6 am and 9 am and again in the evening from 6 pm to 9 pm. The Regionale trains that are guaranteed are trains running during those hours during six days of the week— Monday through Saturday— and do not include Sundays. Regionale trains are designated by the letters “RE” followed by five numbers that identify the specific train on train schedules.

In that case, your best bet is to get to Pisa on a High-Speed train listed by italiarail as guaranteed to run during a strike. From Pisa, you can take one of the Flixbus coaches to La Spezia. You will need to buy your FlixBus ticket online in advance. Ditto for the guaranteed High-Speed train ticket to Pisa, which apparently are sold out for May 5. From La Spezia, the CT towns of Riomaggiore, Manarola, Vernazza and Monterosso can all be reached by a daily ferry ⛴️ which operates from La Spezia from March through November. The ferry does not stop in Corniglia. Other options would be traveling the last few miles from La Spezia by taxi or a ride-share service to reach the towns of the Cinque Terre.
Considering the complexity of these alternatives, if it is possible to do so, it is easier to adjust the itinerary so you can stay put wherever that may be on May 5.