Depends on you settings. From original post:
FP mode supports the full 1920x1080 resolution (SBS and TAB half the resolution).
If your movies are half-SBS or half-TAB, then "same as movie is fine".
If they are full-SBS or full-TAB then you ideally want FP mode.
If you set "preferred mode" to "over/under" and your display supports FP, then that should be selected by default.
Also can you set your resolution (in settings/system/display) to 1920x1080? I think you may be ending up at 3840x2160 when playing video (which doesn't support 3d) and will stop the autoswitch.
A whitelist would allow this, but it seem without a whitelist kodi won't lower the resolution when starting a video.
run "kmsprint" to check which type of 3d mode you are in (it should say one of fp/sbs/tab).