Are you going this week? We were there last week and we saw the forecast for rain this week.
It rained one day during our trip and we went to MK first thing in the morning. It was a light drizzle when we left ASMo but was a steady rain once we got to MK. Yes, despite wearing ponchos we got a little wet, but we walked onto any ride we wanted to go on. We rode Space Mountain, Pooh, Peter Pan, Country Bears and a couple other things. It wasn't pouring, but it was a steady rain. I have to say I didn't love it, but after seeing the crowds at MK the following afternoon, I would say it was worth it going there in the rain. I bet we could have gotten into CRT, CP or LTT for lunch as well. We went to AK in the afternoon when the rain had stopped, and we had the park to ourselves. We even had our own personal safari ride!
One thing we thought about doing if we had another rainy day was to spend the day at AKL. You could eat lunch at Boma or the Mara and then walk through the lobbies and check out the animals. I think I could spend a few hours there relaxing. If you have no kids, you can get a spa treatment as well. They also have a nice lounge if you have no kids.