I am on xbox one. We have 3 profiles on the xbox (all 3 use f1 2020) and mine is not the "primary" one. Here is what happened:
1. Primary user turned off xbox in the middle of grand prix
2. I turned on xbox the day after, switched to my profile, started f1 2020, and I find myself in the middle of primary user's grand prix.
3. I quit to main menu (where in the bottom left it says the primary username, so I know I'm on that profile), go into game settings and change to my user, but in my profile is all of primary user's data and none of my own.
This has happened twice. The first time was not long after getting the game so I didn't take too much notice (there was almost nothing saved on either account); I thought it might have been a mistake on my part of remembering what was on who's profile. This time there were setups for every circuit, some customization, and luckily no My Team yet, but this makes me think it will happen again. Currently on 1.06 but as mentioned it happened on a previous version as well.
Usually if it boots up on someone else's account it says something like "no controller available for [username], please press A to assign controller" and if I switch user, it goes back to the main menu. When I attempted to recreate the issue, this correctly happened everything was fine.