I had all mutators except GC enabled on the KM 2011 vanilla test. My KM dev test I had all mutators enabled.
Perhaps a mutator or setting is responsible? I have altered my keyboard keybinds via settings, unmodded. I do not believe that it is any bug in the code on my end. I am puzzled as to why you cannot reproduce this bug. I will perform the test exactly as you did, since I used my keybind to do the transport (alt+t on mine). Perhaps alt or t may be affecting Felix in some way. I will report back soon.
Edit 1: Some good news. It is in fact the keybind. Alt+t seems to be the culprit. I clicked Transport button and verified it 3x that Felix did not take over the helm. I will do some more tests and try to find a more suitable keybind.
Thank you for the help Defiant. This particular issue has been bugging me for years. Perhaps one day I will look for the files responsible for toggling the Felix autopilot (something tells me its to do with the t, but more testing is required) and try to fix it. Perhaps there is a feature the developers wanted to add that they could not finish, and had to remove, but didnt get all of it out. At least now we know what's the issue here. If you have time, I recommend testing out the alt+t keybind for the Transporter and use the keybind to try to reproduce the issue. I'll bet you get the bug then.
Edit 2: It appears that ANY keybind, whether used with ALT+anykey or just anykey, causes Felix to take control of the ship, overriding user input with regard to piloting. One possible solution would be to trick the game into thinking a keystroke is equivalent to a mouse click on the button. I will do some analysis but not exactly sure what I'd be looking for at this time. First I want to try to fix the missionmenu pys for the multiplayer game modes, as some of the GUI is missing on the right and bottom of the Ships and Bridge selection menus, and when null space is clicked the screen goes black.