Bottom line, the campground has no authority to dictate whether you can use your MiFi device or not. Whether private property or not, they don't regulate the airwaves. Unlike the FCC or FAA that can enforce rules for safety concerns.
Cross channel wireless interference can play a role in routers, but the standard 802.11 protocols are designed to cooperate with each other to minimize such problems. There are many more sources of potential interference such as Bluetooth, wireless controllers and cameras, fluorescent lights, and possibly microwave devices.