For beginner climbs and rock climbing courses in Moab, if you can climb a ladder, you’re good to go. Being in good shape is always a plus but far from necessary. Rock climbing is all about using good movement technique rather than muscling up a cliff using brute strength.
For the more advanced climbs, you have to be in really good shape. The routes are sustained and strenuous, and you should throw out any ratings from sport climbing and the gym once you step outside into the world of crack climbing. You should have an appropriate level of climbing experience and know your limits. Your guide will help you estimate your skill and choose the right route for you.