I certainly can't promise you a guarantee but I've been using it on the wood in my MH for years with no bleaching or staining problems.
It's also the only cleaner I have found that doesn't make me sneeze or go into an asthma attack. So many cleaners add a ton of perfume or add that darn dang Febreeze which is deadly to anyone with allergies.
It's really safer than bleach and water which can discolor some surfaces not to mention items around it and the carpet. Too much room for error using straight or watered down bleach around and on anything.
Just don't spray it on and walk away. I spray and wipe it off. I am allergic to mold or mildew of any kind. So my MH gets a regular dose of Clorox Clean up often. :C