The official fix for this in the Linux kernel has a comment that literally says to assume all x86 processors suffer from the same issue and will disable KPTI for all x86 processors, including AMD.
There's an AMD-specific patch that I saw floating around that keeps the setting enabled for AMD processors, but I'm not sure if it made it into the mainline.
It makes reference to the nature of the bug and explains why AMD's chips are not affected (from an AMD engineer).
The original fix had a comment that literally said, "/* Assume for now that ALL x86 CPUs are insecure */" They've since added a check to exclude AMD processors.
[1] https://kernel.googlesource.com/pub/scm/linux/kernel/git/tip...
Not yet on the mainline AFAIK, but I'd guess that whole branch will be merged soon (before the next release candidate).
Google is failing me or I'd post a link.
AMD has since pushed a patch to "not enable PTI on AMD processors" [1]
I just found it in their git repo, looks like it was added today. https://kernel.googlesource.com/pub/scm/linux/kernel/git/tip...