You can't trust a weather forecast that far out. And 60% doesn't mean rain all day, like others said.
We had rain during our day at the Magic Kingdom. When it rained, we ducked into shops or restaurants or rides with covered queues. We really only needed our ponchos for about 15 minutes. We rode the carousel, Mad Tea Party, It's a Small World, PeopleMover, watched the Carousel of Progress, went shopping, got ice cream - really, don't worry about the rain. You can have plenty of fun even when it's raining.
If you're bringing bags or purses into the park, maybe consider packing a full change of clothes (top, bottom, undies, socks, bra) into a gallon resealable bag for each person. Wear shoes that can dry out quickly, like sandals. The rain might convince some people to go home, so shorter lines! And hey, it's a day at Disney.