We had 2 days of rain when we were there in March. I don't recall anything being closed but then again.....we went seeking the indoor rides and shows. On the second day where the rain was heavier, we spent time in the Marvel and Star Wars areas, and doing meet and greets. We also rode Toy Story Mania....multiple times. And Tron was opened, so I hopped on that as well.
Then we headed over to catch the Tarzan show and the Pirates Stunt show (popping in to Peter Pan along the way because the queue is undercover and we had just enough time before the shows to do one ride). Winnie was closed; otherwise we may have done the same. I don't know if the Crystal Grotto nor 7DMT was opened on this second day. They may well have been closed; but we weren't looking to ride them in the rain so I didn't look.
Roaring Rapids was down for scheduled maintenance.
I would expect that the Camp Discovery rope courses could well be shut in the rain.
Have fun and I hope the rain isn't too bad.