Not all rain is equal
One thing to keep in mind is the variations of rain, especially given Florida and California are two different climates. For Florida, the humidity and tropical storms can be an issue, so rain can vary from "flash" downpours of ten minutes to soaking all day. Even Florida residents can't fully predict how long rain will last or if it starts with little warning, but most of the time it passes quickly. Be warned though: should the rain fade and the sun comes out, it gets pretty hot pretty fast.
For California, it's more likely to get longer rainstorms which vary in how much water comes down. Thus, some souls may be brave enough to go about in lighter rain while others will want to avoid high soaking. It's also likely cooler after some rain, which means wearing layers might be a good idea.
Then there's severe weather, like lightning and wind. In some cases, it might be best just to stick to your hotel than be stuck in the parks during it. That's especially true for Disney World, which has closed the parks during hurricanes.
What's open when it rains at Disney parks?
What rides are open and closed can vary sometimes. Obviously, some outdoor rides are shut down, but others sometimes still remain open as long as there is no lightning or heavy downpour.
For example, when my family visited Disneyland in March 2023, we had a day of heavy rain in Anaheim. Dumbo, Splash Mountain, Radiator Springs, Big Thunder Mountain, the Matterhorn, Jungle Cruise and the Autopia were all open, but Alice in Wonderland, several outdoor California Adventure rides and the Storybook Canal Boats were closed all day long.
It all depends on how heavy the rain is and the length of the storm, as well as the severe weather in the area. With major lightning and wind, several roller coasters and outdoor rides will be shut down, yet others remain open, so it's all the luck of the draw.
By the way, if you have a Lightning Lane/Disney Genie for an attraction and it's shut down for weather, Disney will offer a special redemption to use later. So don't worry about wasting a pass on a shutdown ride.