Wall fasteners

Best way is a screw. No, I'm not being funny. Out in the west it can get really hot in an RV when it is stored without the airconditioning. Really hot, and many glues will give out. Coil-n-wrap sells a high heat Velcro that can be used in many applications. If you cannot screw into the backing (and there are a whole bunch of places that will not hold a screw) you might try cutting a piece of 1/4" ply to make a back plate (the larger the better). Screw the towel rack into the wood then glue the wood to the wall with 3M double sided outdoor adhesive. (sold at most hardware stores).
Good luck, and Happy Trails.