We eventually found a stable workaround.
When saving the map/mask from ChimeraX, use the command line rather than the GUI, and explicitly set the valueType option to either float16 or float32. After doing this, the file can be imported successfully in CryoSPARC 5.0.x.
One important point is that this option was not required before CryoSPARC 5.0. The same integer-type MRC files could be imported successfully in CryoSPARC 4.7, but after upgrading to 5.0.x, CryoSPARC appears to have lost the ability to import integer-valued MRC volumes/masks in this workflow.