All the entities that shill for some lawyer invariably not from your state of residence assure you that registering your RV in their state usually by setting up a LLC violates none of their state's laws. This is, of course, correct. What they don't go into is whether it violates the registration regulations where you live, have your driver's license and/or where you and the RV spend the majority of your time. They also probably have no standing in defending you if you are caught trying to avoid the sales and/or property taxes associated in your actual state of residence and they certainly don't indemnify you against any penalty or costs associated with trying defend yourself if caught. I'd guess these costs would exceed any savings even if your defense is successful.
If you continually travel outside of your actual state of residence and driver's license you might get away with it but if you're in residence more than a month or two at a crack you better have indoor storage where the vehicle license isn't on display and cross the border when heading out as soon as possible.