Emulator

I also tested this with the newest revision at the moment, r6809.
I turned on Sideways Wiimote, started a game (that used a sideways Wiimote), and it worked normally. Then I exited the game, turned off Sideways Wiimote, and started a different game (this one does not use a sideways Wiimote), and the emulated Wiimote still acts as if sideways mode was enabled.

Additional update: with this bug, games that use sideways mode think that it's off, and games that don't use it think that it's on.

Elaborate, which games?
Explain "games that use sideways mode think that it's off, and games that don't use it think that it's on".

I was testing with Donkey Kong Country Returns, NSMB, SSBB, and Fire Emblem: Radiant Dawn.

And sorry about that last statement, I guess I even confused myself...
This issue seems to only affect games that do NOT use Sideways Mode. So let's say Super Smash Bros. Brawl.
If I turn the mode ON, it acts as if it was off. But when I turn the mode OFF, the game acts as if it was ON.

This IS working properly for games that do use Sideways Mode, Off is off, On is on.

What do you mean "it acts as if it was off/on"? How does the game "act"? Which extensions are you using? And again, list the game in your explanation.

No extensions will be used at all, at any time.

So let's say I am playing New Super Mario Bros, and since that game uses a sideways Wiimote, I will be enabling Sideways Wiimote. It works as expected.
Then I decide to play Super Smash Bros Brawl, which doesn't use a sideways Wiimote. I will be disabling sideways Wiimote. But the game, SSBB, thinks the Sideways Wiimote option is on, therefore when I press DOWN on the Wiimote, it goes RIGHT instead.
Re-enabling Sideways Mode will then make all the controls function normally in SSBB, so RIGHT is RIGHT, and DOWN is DOWN.

That is what I mean by the game acts that way. If I am still being unclear, please tell me so that I will try to record a video to demonstrate.