Forcing DirectX9 has worked for some people.
Try:
Go into your steam library
Right click rust., then select "properties"
Then click "Set Launch Options"
Type in "-force-d3d9" (without the ")
Press Ok and try launching the game again.
If this doesn't work, then I can't help you anymore. You just have to search for AMD related issues with this game on this forum.
And please join playing on Redkids PVP Sleepers server :D
Hey KaiO, thanks for trying, but unfortunately this made me unable to join any game. It'd crash just as I was about to load in.
Anyone else have any ideas?