The last person to maintain these Red Hat servers somehow set it up so they stay in sync -- if I delete files on one it automatically deletes them on the other. I need to set up a new configuration on just one of them, so I need to disable the synchronization, but I don't know what's causing it. Where should I look?
The most obvious way, especially if the synchronization is instant, is that they may be using a network filesystem. Confirm that you're not looking at an NFS, AFS, etc. mount.
Now, if its not instant (or even if it is, some of these programs are fairly quick), there are several tools that do this; possibly the most common is
There are a bunch of commercial offerings, too. Looking at /usr/local, /opt, and installed packages may help here.