SRT Aviation at KMVN Mt. Vernon, IL is a very pet friendly FBO and have given animal rescue pilots fuel discounts. Just let them know you are on an animal rescue mission. Both Shawn and Rich, the owners of SRT Aviation, and the Manager of Mt. Vernon Outland Airport are very supportive of the animal rescue program. I know because KMVN is my home base airport and we take animals through there on a regular basis.
KDCU, Decatur-Athens, AL were friendly and allowed animals to be loaded at the plane from a vehicle, but no fuel discount. KJVL, Janesville Jet Center was friendly, allowed rescuers out to the plane and back through the lobby with the dogs, but no fuel discount. Paducah, KY (KPAH), Rolla, MO (KVIH), Olathe, KS (KOJC), Kirksville, MO (KIRK) were all friendly, allowing rescuers and animals access to the plane, but none of them offered fuel discounts.