You have used chroot so the only thing that yum is using is the kernel from the "live distro". The things that yum is going to want to do are pretty standard, open files, read files, write files, launch programs, allocate memory, and this will work for any kernel from say the last 10 years assuming that it is for the correct architecture.
You might want to ...
First, x11 clients need to talk to the x11 server via a socket file, usually
# mount -o bind /tmp/ /srv/stable/tmp/
Second, xauth I mean, xhost which I keep confusing together.
either A, (Recomended) the uid of the process inside the chroot must
match the uid of the user who owns the xauthority on the host, for
example we can ...