Issue with /etc/gdm/*
In looking at the GNOME Display Manager Reference Manual I noticed several directories under /etc/gdm with different scripts and such.
There are a couple of references in these directories to $HOME. I'd try commenting those out to see if you can get rid of the access to $HOME.
To debug your issue further I'd be inclined to throw a couple of set -x lines at the top of the various scripts in these directories to see what's running prior to the "permissions denied" messages.
The script in the directories are all bash scripts on my systems.
/etc/gdm/custom.conf
debug option
There is a debug option in this file that is disabled by default. Try enabling it, the messages will show up in /var/log/messages.
[debug]
Enable=true
Disable faces in login
I'd also try disabling the inclusion of all user's faces at the gdm login in the face browser.
[greeter]
IncludeAll=false
Instead of disabling it you could experiment with disabling just one of your problem users by adding them to this list:
Exclude=<some user>
Update #1 - bugzilla issue
The issue appears to be related to this bug filed against the Red Hat Issue tracker, titled:
There is no resolution but as part of the bug there was a test to confirm that you were experiencing this bug.
When the problem shows up GDM apparently creates a cache directory here: /var/run/user/42. Deleting this directory allows GDM login to proceed. The OP has confirmed this in the comments.
Update #2 - possible workarounds
There was a 2nd comment (by me) to some additional links with suggestions to work through the issue. The link titled:
specifically in this section:
had some modifications to the PAM setup that might fix the issue.
Best Answer
On my system
psfinds this:The display manager starts X with the auth file to use as parameter. It can use that file directly.
Edit 1:
It's KDM in my case, not GDM.