My two cents: (I did not duplicate your issue and I do not want to try)
when you are running Guix in a foreign distribution, you may not want to have Guix active in your login shell by default... That may mess up your UI environment, Since you have issue with GDM, I assume you set up Guix to be active in your login shell script. Avoid that. Guix has its own glibc and your programs in the foreign distribution like GDM may misbehave if you have Guix libraries in the path.
I would run Guix GUI programs from a terminal once you log in to your desktop, then manually activating the Guix user profile first in the terminal.
This probably is not related specifically to g-golf. Just my guess.