"I don't understand how only radeon driver can cause such problems"
Because, on newer kernels, the radeon module is known to fall over and die when the proprietary junk isn't present. You can thank the Linux kernel developers for that.
And not necessarily for any good reason. In some cases Linux-libre changed the firmware loading to a conditional instead of an outright failure and it worked just fine. Although this may not be the case for all of them.
