Phil,
Thanks for responding. When I open Mail.app normally (not "safe mode") it often hangs within a few seconds. When that happens the activity window shows many instances of "opening mailbox" which never go away. No indication of which mailbox in activity window. When that happens Mail stops properly showing mail lists and message contents. You can click from one mailbox to another, but that has no effect. Thus the symptom that all mailboxes seem to have the same contents. In other words, I think that's a symptom, not the problem. I'm not using Kerberos, as far as I know.
As suggested by bthomp2420 on this page, I did this: "Try deleting the contents of ~/Library/Caches/com.apple.iCloudHelper and then kill the com.apple.iCloudHelper process in the activity monitor."
I thought that had worked because I was able to open Mail several times without a hang. But subsequently the problem returned and I'm now assuming that the success was just random luck, because the problem has been intermittent.
I've been using Mail for a couple of weeks now by holding down the shift key when I launch it. That always works, but I have no idea why, and no idea what to do to solve the problem. If you have any suggestions, please let me know.
Thanks again --
Steve