>>532177013
None of the Prime Rouge AU counterparts have any interest in gems whatsoever.
Rebel would think it's a waste of time when she could be helping to protect the world from the Chaos Council. She gets furious at Sonic any time he shows any amount of leisure or playfulness.

Prim is more of the same. Her only priority is protecting her tribe. Both of these Rouges are humorless and down to earth.

Baton? She gets angry at Sonic for prioritizing the crystal gem at all while they're endanger.
If Prime really is canon, then loving gems is not integral to who Rouge is the way intelligence is integral to Tails.