This is caused by folding wings being turned on in the Level-d 767. Does GSX activate folding wings?
GSX doesn't activate anything, and surely doesn't send any key presses for the precise reasons that if it did (like for example, if it tried to operate doors automatically) it COULD cause side effects like these so, GSX only READS simulation variables, it never WRITE them or send key events.
That's why I've said it's not possible that GSX could have any effect on a 3rd party airplane.
The only possible interaction of keys, is if another addon is using the same hotkey as GSX (CTRL+F12), this results in one of them not working, depending which one is loaded first, but this should be fixable easily, by changing the key assignment either in GSX or in the other addon.
The default key for Wing-folding is CTRL+Shift+K, so it seems unusual that would cause a conflict with CTRL+F12