Although not directly addressed in the Boarding FAQ, not only are you allowed to change seats, but it's the norm on a stop, after the disembarking passengers are deboarded. In fact, sometimes the flight attendant needs to ask people to remain seated for a minute so that they can get a headcount.
Southwest Airlines has no assigned seating anywhere; not only can you not reserve or purchase a specific seat assignment, but there is no way for anyone to guarantee they will get a seat in any particular part of the cabin— front, emergency exit row, aisle, or otherwise. According to SeatGuru, Southwest does not have bassinets, so you won't be kicked out of a bulkhead for that reason, either. Once you're aboard, any unoccupied seat is yours for the taking.
Programs like Business Select, A-List, or EarlyBird can only get you an earlier boarding position; once you board, you're still subject to availability. Even if you're A1, then, it's always possible that you board to find someone else sitting in your favorite seat. It's part of the Southwest culture.
It goes without saying that you must be qualified to sit in an emergency exit row to sit there, of course. Furthermore, the flight attendant can always reseat you for other reasons, for instance if a certain seat is the only one that can accommodate another passenger's medical equipment.