The issue is not so much about owning property as about where you declare your domicile when you go full-time. For example, if you want to become a resident of South Dakota while full-time RVing AND own property in South Dakota, also owning property in another state is not an issue because you have established a connection to South Dakota. But if you want to become a resident of South Dakota for purposes of full-time RVing, and do NOT own property in SD, but own property in another state, that might be a little tricky. I believe that most full-time RV'ers divest themselves of property before establishing their domicile in an RV friendly state, as it just makes life less complicated.
I am not an attorney, so I can't really address the legalities. My advice is to check on residency requirements for the state you are considering making your domicile as each state might be different. Consult an attorney if you have a complicated issue.