What ever you use, DO NOT USE ANYTHING WITH CLOROX/BLEACH IN IT! I used it on mine and all the stitching rotted out in 6 months time. I never could get mine to come clean and eventually replaced it when the threads fell out. I spoke with my top guy and he took one look and told me I was parking it under trees. Yep, trees kill a top quickly. Even if you can't see it, it gets sap on it that molds up.
With my replacement, the first thing I did was use RaggTopp cleaner and protectant. You might can try the cleaner, but if your mildew is set, I don't think anything will clean it.
My top is 3 years old this month, still looks like the day I installed it since I never parked under trees and I used Ragg Topp on a regular basis. Unfortunately, all that care was a waste of time. Had a woman cause a 4 car pileup on the interstate and my '95 totaled in August. I'm planning on parting out the car here soon and hoping someone needs a complete top.