I've come across a peculiar issue when playing on Xbox Series X using a standard Xbox Series controller.
In mid-flight, with auto pilot engaged, I go into cockpit view and press LS to activate cursor mode so that I can use LS to look around the cockpit and manipulate the instruments and controls. When I move the LS while in cursor mode it's as if I'm still in "control" mode and as soon as I touch the LS, the aircraft responds accordingly (dive, climb, bank, etc.).
If I exit cursor mode by pressing LS I can control the aircraft as necessary with the LS; I enter back into cursor mode, move the LS and the aircraft again responds accordingly.
This only started recently if I recall correctly, I mainly play on PC with a mouse/keyboard/HOTAS setup, but enjoy flying casually on Xbox now and again.
I haven't started any specific troubleshooting yet, but will try swapping the Xbox controller for a different controller, resetting my Xbox controller profile back to "Default"in MSFS, and deleting the MSFS 2020 data from my Xbox profile. Not sure what else to try and Google searches don't provide much help.
Hoping someone else here may have seem this and figured out how to fix the problem.
Pretty sure I had the same experience today, but I was too tired to really get stuck into a proper session.
Will try and replicate the issue tomorrow and will update if it's an issue as well.