You can use BitIO and BitIO both with and without an RTOS, it does not matter. The BitIIO_LDD is more 'tuned' towards if you are using MQX, but really: an RTOS should not make a dependency on drivers, or use an abstraction layer, like the Kinetis SDK.
Mentioning the SDK: if you are using the Kinetis SDK, then there is a third category of components, the fsl_xxx ones. If using the Kinetis SDK, both the BitIO and BitIO_LDD ones are not available (working).
As for the SPI: I prefer to use the SynchroMaster component, as having an easier API and easier to use. But it is up to you: you can use the one or the other.
Erich