Specifically, I want tags in org mode to be a variant of the color of the corresponding heading (e.g. less saturated or lighter).
Each org mode heading level is a different color, so I can't just directly change the color for the org tag face.
I can clearly inherit a variant of the size, but there doesn't seem to be any way to inherit a variant of the color. Is it possible?
No, you cannot set a face to always be a certain amount lighter or darker than the inherited face.
You can not customize a face based on context either.
If you would like org tags to change color based on their location in the org tree, you will need to use a custom font-lock keyword function that programmatically apply colors to org tags based on location.
See the function and (matcher . facespec) sections of this document specifically:
Search Based Fontification
