We have a cat tower or condo or whatever people call them these days in our Class-C. It has three shelves. My husband screwed it into the floor. It depends on how they're made as to how easily they topple. We have 5 in our house and one in each RV. When my male cat took a flying leap onto the one in our sunroom at home, it did topple over - fortunately nothing was damaged and he was not hurt.
Be very careful with cats and RVs. They're known to bolt out a door which can prove fatal for them. Use a spray bottle of clean water to train them to stay back from the doors. It's so sad to see the cats left behind in CGs. Several Hosts have told me they usually die off when the CG closes at season's end or when winter comes and there aren't enough campers leaving food for them.
And a reminder to NEVER but NEVER move the slide in or out when cats are loose. Make sure they're in their carriers or closed in the bathroom before moving the slide/s.
When on the road it's safer for cats to ride in carriers or large cages as they can become flying missiles in an accident or if the brakes have to be used suddenly and heavily.