Those back country campgrounds are the ones I use MOST OFTEN and it is a common thing to find these totally unmanned campgrounds saying "no checks". You simply put the "CASH" into a device that is labeled "Iron Ranger" until they pick up the money (often only once a week or so).
I occasionally use checks in these type of campgrounds and it's never been a problem for me. Usually I'm not even there when they empty the "Iron Ranger" as they call it but on the occasions when they did, they take my checks with no comments. I have always made a HABIT of writing only GOOD checks though but doubt if they check, other than running them through the banking system for payment. Have noticed that it takes sometimes a month or two for them to clear my bank. The no check policy comes from people a lot higher up the food chain than the local ranger who is just doing his job of emptying the cash collection boxes.
I TRY to always have some cash in the RV for this type of purchase but since I carry almost NO money at all otherwise, I am sometimes caught without change or without cash at all and a check has always served me in those cases. The no check policy makes PERFECT sense since with nobody around to even verify identity it would be totally foolish to willingly accept checks. I'm much MORE apt to become angry when I see our government do something foolish (like taking checks from a total stranger with no id) than when to do what any person with any sense would do.