Rage (as well every OpenGL/id Tech 5 game) is famous for terrible performance and loads of issues in AMD hardware.
Since Radeon driver 22.7.1, AMD rebuilt their OpenGL driver from the ground up, delivering better performance and stability in all games that use this API.
I'm playing this game right now with driver 23.5.2 and the game is working perfectly. I'm even playing the 32-bits version (without mods), and everything is running fine.
Have anyone tested out newer drivers and got success playing this too? If yes I think it's valid to clarify this on the "Regular crashes with ATI/AMD desktop and mobile graphics" topic of the issues unresolved of this game.