Lots of experience, plus, we've been to Alaska, too..
The only precaution to take around your campsite is to put away your grill locked in the truck of your car, along with a cook stove. Keep a very clean campsite/table - no dirty dishes and obviously, no food left out. Definitely do not leave a cooler out. All of the above will get checked by the rangers and hosts and you'll hear about it if you don't adhere to it. There is absolutely no worry with food inside your RV. Everyone has food in their RV. This all should not be a big worry for you. Go and have fun!!!