Well, it is a little bit of both.
Yes, the CLASS or Classification of the Government property comes into play, as there are a variety of methodologies that may be used for different types of property – material may be identified differently (Labeling the box, bag or bin) versus general purpose equipment where a label or plate may be applied.
By the same token the composition of the item MAY also affect the application of some form of identification. Yes, I agree with you that "…you wouldn't etch or stamp into glass." That might cause some breakage.
But, the FAR GP Clause, 52.245-1, does not require that as part of the IDENTIFICATION LABEL or TAG a statement as to the material composition of the item. That information MAY be contained elsewhere and used for other purposes.
The Government is concerned that the contractor have a PROCESS with an OUTCOME that deals with the APPROPRIATE IDENTIFICATION of the GP – appropriate being interpreted as suitable for the:
CLASS of GP AND
Based upon its physical characteristics.