I don’t mind getting a bit wet, but NOT from the steam bath that happens to me in a poncho or raincoat. My little umbrella was my best friend during a 10-day trip with long periods of rain EVERY. SINGLE. DAY. Make sure that whatever footwear you choose will stay in place on your feet. Think sandals with decent straps unless you are going to switch back and forth from flip-flops to dry shoes (which I would find a real PITA!) Sandals are my choice of footwear but will become slippery on your feet when wet, which both slows you down and can be dangerous.
Most of all, embrace the rain if it is going to continue for long. Wade through the puddles and relish the drastically reduced crowd! I will forever cherish a memory of my DSIL, holding my DGS (7 at the time) by the hand and skipping toward 7DMT in a downpour. They were going back for their fourth turn, and loving every minute of it! Earlier, we had our very first ride on this attraction while we were all dry. Just as we crested the first rise and the train hit the outdoors, the heavens opened up with a vengeance ! After the initial squeals of dismay, the whole trainload sang “Hi Ho!” At the top of our lungs for the rest of the ride. To this day, we remember that as our best ride ever on 7DMT.
Anyway, just make sure that you have a way to protect anything that would be damaged by water, or that needs to be kept dry so you can be comfortable after the rain stops. Being wet, or even damp, in an indoor venue with a lot of A/C is a sure way to get a chill. Ziplock bags in necessary sizes are your friend. Renting a locker can be a huge help. I am also now not adverse to buying some dry t-shirts or hoodies if the situation required it, but that did not always fit into my budget.