We were in WDW from 6/26-7/3 of this year and the weather forecast was "chance of thunder storms" each day. We had rain each day but 1, every other day it rained in the afternoon, not too long we just put on our ponchos and kept on going.
There were 2 days when we had a pretty good storm, on our e-ngiht day it rained hard and there was thunder and lightening, we were in MK and were talking to my son who was still at the POFQ and it was not raining there. It rained hard enough to slow us down, we took shelter in the Tiki birds and then the Hall of presidents, by then it was time for our PS at the Plaza so we ran over there. But it had stopped raining while we ate. Our last day the 3rd of July it rained in the late afternoon, from around 4 until we left, again some times it rained really hard and thunder and lightening. We left Epcot around 7:00 and it was still raining lightly. But except for when it was pouring it really did not slow
us down. One night we were afraid that they would have to cancel Fantasmic, but the storm cleared up and everything went on as planned. I think Spectro had to be cancelled one night, but it ran each night so it did not affect our plans at all.
Just make sure to have a poncho each day and you will be fine.