We just came home last night from a rainy week all last week in Disney. When we saw the forecast the week before we were in the same boat worrying about it, but it was fine.
Bring good ponchos (not the clear, thin ones from the dollar store), extra shoes (if you wear sneakers) and just be prepared to go with the flow. If you don’t have a good weather app on your phone, get one now to keep an eye on things. Disney will usually run the outside rides in the rain but will definitely close them if there is lightning in the area. So prepare to get on the outside rides quickly if you know a storm is coming in. We had a FP for 7DMT and made sure to tap in five minutes before our FP opened because we knew a storm was headed our way. Sure enough while we were in line waiting they kept making the announcement that they may have to close the ride suddenly. Thankfully we rode with no issues but this is an example of just preparing a little bit ahead if you can.
Honestly, the most important thing we learned is the forecast changes quickly, sometimes hour by hour, and it won’t be as bad it looks. In spite of the rain, we had a lot of breaks was full sun and got to spend time at the pool on a few days.
We usually go to WDW this time of year and it was the first time we had these cooler temps and so much rain for a whole week. We still had a great time! You will too!