Here is my rainy tournament list:
1 - Big umbrella: gives you dry space to set your bag while throwing and while drying discs.
2 - Extra towels: I usually go through 3 in a wet round wiping off a disc after every throw.
3 - Birdie Bag: use it when a power throw is needed, you don't want the disc to slip out early when you are gunning for 350'+
4 - Waterproof shoes: if you don't have any, at least get some spray-on waterproofer.
5 - Change of clothes and shoes: the thought of being dry and warm on the ride home always improves your outlook for the entire day.
6 - Patience: Throw, wipe, repeat. Take the time to completely dry each disc before returning it to the bag. That way you always have dry discs.
7 - A plan: Plan for all of the above, and don't set ouot to break any records. Aim for a solid round, nothing fancy but also mistake free.