Is there any port for X86 in protected mode? As far as I know FreeRTOS x86 is real mode only. Is there any official or no official port for protected mode?

Not that I am aware of, but you might get lucky. FreeRTOS is designed for microcontrollers, hence there is a real mode port (for 186 based microcontrollers), but I would not create a protected mode port myself as that is out of the primary application domain (although FreeRTOS seems to be getting popular on ARM A9 cores now).

Regards.