If a SID chart says "GPS... required", can the plane use a different GNSS? This US/FAA standard instrument departure says "Note: GPS or DME/DME/IRU required."

If the aircraft could tune into a different GNSS like GLONASS, could the pilot still legally fly the departure given that all other requirements were met?
The FAA's standards require the use of GPS, i.e. the American satellites. This is covered in AC 20-138D, Airworthiness Approval of Positioning and Navigation Systems. It defines GPS:

k. Global Positioning System (GPS). GPS is a U.S. satellite-based radio navigation system that provides a global positioning service.

It also says that GLONASS and other non-US systems are not supported:

GLONASS is not yet approved for IFR operations in the U.S. National
Airspace System
[...]
No FAA TSO exists for GLONASS, GPS/GLONASS, multi-constellation or
dual-frequency avionics. Therefore, adding capability for any other
constellation or dual-frequency capability must be accomplished as a
non-TSO function until appropriate TSOs are available.

Apparently there is some kind of working group looking into using non-US GNSS but it's not possible yet. See Appendix 8 of the doc for full information.