When I as a GM want to look into a particular tab of a character sheet (of one of my players), this currently automatically changes their view. When they don't have the sheet open at that point in time (and I forget to go back to the main tab), they will see the tab I chose next time they will open the sheet. My suggestion is to separate the visibility and only store the players choice with the character and the respective sheet. For the GM it is OK to hop to the tab they need every time.