I am not familiar with all the states but were some states right hand drive and some left hand drive. Here in B.C. up to about 1915 all were right hand drive before the transition to left hand drive.
I believe that in all U.S. States the roads were always required to be driven on the right (once traffic laws were established).
Cars were not legislated to be either right hand drive or left hand drive. Prior to 1909 most cars were right hand drive (r.h.d.). Subsequently, due to the influence of the model T Ford mostly, almost all vehicles were left hand drive. Specialty vehicles like postal delivery vehicles are still produced r.h.d.
When I had a r.h.d. model T I was never stopped by a constable... R.h.d. is not illegal.