Can't log in on console as anything but root

Not sure if this is a security or networking issue, but here goes:

We have a number of Redhat 7.3 Linux PC's on our network.
Until now, they have only been used via remote logins from Sun Workstations for the purpose of distributed processing.

Therefore until now, the only login on the actual console has only ever been with root.

Now, due to a change of requirements, the Linux PC's have been deployed on desktops and the users require local logins.

However, the Redhat Login screen on each PC will not allow this - the screen simply blinks and returns to the login prompt for anything but root. No errors are logged in the message file.

If we do log in as root, we can easily use the su command to change to any other account - but why can we not do this from the initial console login?

I am not completely sure but I think this might be because of users not being in some user group. I am not sure about this but can you check what groups are the users trying to login are in?