It does seem straight-forward but essentially what you are asking for is a multiband mask to match the multiband file.

There isn’t a tool to identify and update “bad” pixels within a hyperspectral scene. There is a 'Replace Bad Values' tool where you can set pixel values but it does not work per band.
It would not be that difficult to implement a routine to do this in IDL, if the pixels you are looking for are easy to find (i.e. a certain value far outside the data mean). If you can find them, you could replace those pixels with NaNs or other unique value that can be set to the 'data ignore value' and ENVI would correctly ignore those pixels for most processes.

ENVI does support a pixel value state for *any* pixel in a raster, so if the raster has multiple bands, your pixel value state is three dimensional as well but we don’t support *saving* this information to disk. ENVI has only ever supported the idea of a single band “mask”.
https://www.l3harrisgeospatial.com/docs/programmingguideworkingwithrasters.html#RastPixelState

Hi Mari. Thank you for your answer. I was able to do replace the values in question using pygdal. However, now I am running into a related issue. If I set the value for a specific band in a specific spatial pixel to either 'Nan' or to the data ignore value specified in the header, ENVI will then ignore that spatial pixel completely when I compute a mean spectrum over an ROI. How would I get around this? The idea is to be able to get useful mean spectra of a spatial region, not letting spurious values in a specific band of a specific spatial pixel affect the mean. However, the way it currently seems to be working, it throws out that entire pixel in the ROI calculations, which would essentially be the same as just removing that whole pixel using a mask.