Is it possible to use a Shimano 12 speed micro spline cassette with a SRAM Eagle 12 speed chainring, derailleur, and possibly chain? Or are there any incompatibilities, such as a Shimano chain also needing to be used?
SRAM and Shimano 12 speed are cross compatible. The pull ratio is slightly off (offhand I believe it’s 1.76 for SRAM vs 1.7 for Shimano), but it seems to work fine in the real world.
To get the nice Shimano “Hyperglide+” shifting, you would need both a Shimano cassette and chain. It would shift without it, just not as well.
Of course, you cannot use SRAM XD cassettes on a Shimano MicroSpline freehub body or vice versa.