Don't let the rain slow you down! We always keep going by just throwing on our rain ponchos (we wear flip flops, too, in case of rain). When our children were little and still in strolllers, we had purchased rain covers for the strollers as well. Our policy is to just keep going, rain or sun.
The weather has to be extremely bad for the parks to close, such as a hurricane (we actually had this happen to us once; they brought characters to the resorts, movies on tv, games in the lobby, etc -- it was still just as magical). But chances are in May, this shouldn't happen.
There can be some rides that do close, but many just keep going. We find that Epcot is a perfect place to be during rain since nearly everything is indoors. And one of the best things is that with rain guests leave; the crowds can be cut down in size so quickly. Downtown Disney is also a great option on rainy days.
Nearly all of the character meet and greet areas are enclosed, so rain shouldn't keep you from meeting them.
Sadly, the parades are sometimes cancelled to keep the cast members safe. But the evening we were there as the hurricane was coming inland and pouring rain, it let up just in time for the parade. it went on as planned!
Overall, don't worry about the rain. Have rain gear (it will be for sale everywhere if you need to purchase it at the park) and don't let it keep you from enjoying yourselves.