The short answer
Does rain stop a roof replacement?
A little rain can pause the job. A torn-off roof should never sit open to the sky overnight.
Roofers plan around rain every week in Florida. They do not tear off the whole roof and hope. A good crew checks the forecast, strips only as much roof as it can cover the same day, and puts a waterproof layer on the bare deck before it leaves. The deck is the wood sheet layer, usually plywood, that the shingles or tile sit on. That waterproof layer is called dry-in.
Wet wood is the first problem. The Florida tile installation manual from FRSA and the Tile Roofing Industry Alliance says not to install underlayment over wet surfaces. Underlayment is the layer between the deck and the roof covering. So a crew cannot just roll it out on a soaked deck and call it done. If rain starts before the deck is covered, the crew has to cover what is open and wait for the wood to dry.
Some crews cancel the morning when the forecast looks bad. A Journal of Light Construction article on tile reroofing says its crews may cancel when the morning forecast shows a 60 percent or higher chance of rain, because the roof is torn off and covered within one day. Your roofer may use a different cutoff. What matters is that there is one, and that you know it before the job starts.
This page explains how rain is handled, what the dry-in layers can and cannot do, and what to ask your roofer before the crew shows up. It is general information. Your contract and the manufacturer's instructions for your roof control the details on your job.