Hi Pancholina2021,
Welcome to the Forums!
As others have said, tile in a motorhome is not usually a good idea. Now if it was a large, heavy DP (diesel pusher) with air suspension and strong, rigid floor and walls, that might be different. Plus tile & backer board is heavy, and weight is quite likely something you should try to minimize in that rig. And, of course, that heavy tile and backer need to be securely fastened. Walls in most RV's are not known for their strength. They separate one space from another, hide wires & plumbing and hold switches and stuff. But don't ask them to support shelves or heavy objects like the walls in a stick-built home can do. (Come to think of it...I don't know how well those walls would do either, if they got bounced down the road at 45 MPH! LOL)
While we don't know the general condition of the rig you inherited, a 40+ year old motorhome might have limited life in it, depending upon how much money you're willing to throw at it when things fail.
My recommendation is to get if functional using the lightest and cheapest materials which are easy to install and readily available.
Again, Welcome & Good Luck,
~Rick
2005 Georgie Boy Cruise Master 3625 DS on a Workhorse W-22
Rick, Gail, 1 girl (27-Angel since 2008), 1 girl (22), 2 boys (23 & 20).
2001 Honda Odyssey, Demco Aluminator tow bar & tow plate, SMI Silent Partner brake controller.