You can skydive in the rain but it's not really safe to skydive in the rain.
Actually skydiving in the rain is against the FAA rules and regulations because the rain and clouds make it hard to see and reduces your visibility.
Visibility is very important to pilots as well as skydivers so any legit skydiving operation will not allow skydiving during rain or thunderstorms.
Of course you could go up in a private plane during the rain and skydive but you may get fined if you do get found out.
But any skydiving company I've heard of does not take you skydiving during rain or storms.