my Yum repository doesn't have anything newer than glib-2.0.
But glib is a fairly core animation library, is my understanding. Is there an easy way to upgrade that won't brick my system?
As far as I am aware, a glib upgrade will require a gcc upgrade. If you can't find an upgrade inside your repository, don't even consider doing this from source; you don't upgrade gcc yourself without risking breaking your system.
If you can find a repository that provides it which is third party, proceed with caution.