Solved.
1. Run "sudo setenforce Permissive".
2. Download and install
Skype for Linux.
3. Type "skype" into a terminal. You will likely have missing libraries. Use "yum whatprovides <library>" and install the packages it recommends. Repeat this step until Skype starts.
4. Download the
pidgin-skype plugin.
5. Extract deb. Move *.so to /usr/lib64/purple-2
6. Paste the following into /usr/share/telepathy/managers/haze.manager
[Protocol bigbrownchunx-skype-dbus]
param-account=s required
#param-password=s required
7. Start Empathy. Add a new "bigbrownchunx-skype-dbus" account.
8. Delete /usr/share/telepathy/manager/haze.manager. Do not close Empathy.
9. Delete the account you made in Step 7. Do not close Empathy.
10. Add a new "bigbrownchunx-skype-dbus" account. This time a Skype window should pop up asking if Empathy can use the Skype API. Allow this.
11. Your Skype contacts should now be available in Empathy.
---------- Post added at 11:23 AM ---------- Previous post was at 12:51 AM ----------
Stopped working after a restart. I found a workaround, though. After logging in, run "sudo setenforce Permissive" and then start Empathy. Skype will autostart when Empathy loads, and the contacts will load in Empathy. Not sure exactly why SELinux needs to be permissive, but it works.