Felt bottoms on your waders should not be used in Florida. But removing the is an issue that threatens the stability of the waterproof waders. You have only two options, though.
One is to cut the felt sole off, which I do not recommend. The second (best) option is to coat the felt sole with urethane caulking. The urethane is flexible and good in all temperatures. It is also very strong, wear proof and waterproof. It should have some gripping capabilities and be slip-resistant.
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Captain David M Rieumont
You can check out Captain David himself from his incredible and very popular Patriotic Angler podcasts. They cover every bit of fishing you can imagine, and there are new ones being created constantly. David and his team remain one of best resources any fishing community has anywhere in the country.