I'd worry about this when traveling solo. With a companion it would be easier to use the showers with someone else to watch over the campsite. A friend of mine rode cross-country alone and has done several weeklong loops here in the east and only once did he have trouble; he caught someone trying to get into his tent when he returned from the showers.
I've had items removed from my handlebar bag when the bike was locked up briefly while I was in a store.