The View/ExtractBrain menu item will call FSL's BET Brain Extraction Tool. This should handle NIfTi spatial orientations fine.
  https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/BET/UserGuide
However, be aware that some FSL tools will flip the way images are stored on disk to ensure a negative determinant. These flips are stored in the NIfTI header, but can confuse tools that ignore the NIfTI SForm/QForm:
  https://fsl.fmrib.ox.ac.uk/fsl/fslwiki/FDT/FAQ#What_conventions_do_the_bvecs_use.3F

The View/RemoveHaze should also preserve spatial orientation, though disk order may be changed for RAS storage. Again, the modification is stored in the SForm/QForm, so it is lossless.