Root users can log on to RHEL. Users cannot!

Root users can log on to RHEL. Users cannot! -- Linux general technology-Linux technology and application information. For details, refer to the following section. I used GNOME.
When logging on to a user, the following message is displayed:
However, you cannot write your authentication file. This may mean that your hard disk has no space, or your home directory cannot be opened as a write. In either case, you cannot log on. Contact your system administrator.

The first case is definitely impossible, and the rest is about permission settings. How can I set permissions for the home directory and its user directory?
Thank you!
You can also log on to the character interface. But cannot log on to the graphic interface!
When logging on to the character interface, a message is displayed:
ID: cannot find name for group id 501
What's the problem?

[ This post was last edited by ireed]