Looks like you have a rubberized version. Yes, rubber and alcohol are not compatible. Have you ever looked for an acetate or Teflon diaphragm? There are kits available and depends on how old the engine is and which diaphragm you're talking about.
Official B&S: Shop.briggsandstratton.com for OEM diaphragms/kits, some of which may be Teflon.
Aftermarket: Amazon, eBay, Jack's Small Engines, BMI Karts, or Oregon kits. Search by your exact model/engine number. There are plenty of aftermarket kits that are ethanol resistant.
Forums like SmokStak, ArboristSite, or MyTractorForum often discuss adaptations for specific engines.
I've even made my own out of specialty Teflon sheet for smaller carbs or just flat out replaced an old carb for something using more modern. Ethanol resistant materials.