Created attachment 584262 [details] compressed build log cairo built just fine then in install phase bombed with headers being different, and mentioned ABI changes. I have no idea what to do with this. I looks like a duplicate of 596866 but that one involved directfb in USE flags.
Created attachment 584264 [details] emerge info
# emerge -pqv '=x11-libs/cairo-1.16.0-r3::gentoo' [ebuild R ] x11-libs/cairo-1.16.0-r3 USE="X glib opengl svg xcb (-aqua) -debug (-gles2) -static-libs -utils -valgrind" ABI_X86="32 (64) (-x32)"
Created attachment 584280 [details] 32 bit configure log
Created attachment 584282 [details] 64 bit configure log
In the 32-bit configure log, it says Fontconfig: no (requires fontconfig >= 2.2.95) and in the 64-bit configure log, it says: Fontconfig: yes I don't know why this happens exactly, but in a previous report the user recently transitioned to the 17.1 profile. I assume you did not re-emerge fontconfig (emerge /lib32 /usr/lib32 -v1 is what the news item suggested doing). As a result Cairo now cannot find fontconfig in the 32-bit case.
rebuilding fontconfig did allow cairo to install. I did do the emerge /lib32 /lib64 but it may have failed without my noticing.