Due to a conflict between two instances of Thunderbird ...

Please explain that in more detail. What conflict exactly?

... that unintentionally shared the same database

What database? Are you talking about the Thunderbird profile?

I ended up with two Inbox folders at the top of the left pane

Please post a screenshot. https://support.mozilla.org/kb/how-do-i-create-screenshot-my-problem

What is the account type - POP or IMAP?

Thunderbird is installed on two Macs, both of which reference the same profile directory tree in Dropbox. Normally Thunderbird is only used on one Mac at a time. However, clicking on what was not known to be a mailto: URL caused Thunderbird to launch on one Mac when it was already active on the other. This caused duplicate folders to be created in Thunderbird.

The account type is imap.

See attached for a screen shot showing the duplicate Inbox folders. I'm trying to delete the second Inbox folder, but am unable to rename or delete it.

Thunderbird is installed on two Macs, both of which reference the same profile directory tree in Dropbox.

Sounds like a really bad idea to me, particularly with an IMAP account. So whole point of using IMAP is that multiple clients can access and sync the data on the server.

When logging in to your account via webmail, do you also see the extra Inbox folder?

I agree that it's a bad idea, and will be changing it so that Thunderbird on the two machines don't share files.

When I log into webmail on my mail provider's site, I do *not* see the extra Inbox folder.

To determine the profile location see https://support.mozilla.org/en-US/kb/profiles-where-thunderbird-stores-user-data#w_how-to-find-your-profile

Navigate to your profile folder - ImapMail - <your_imap_server_name>.

In that folder look for files named INBOX. Please post a screenshot of your file manager window with the contents of that folder (and any INBOX files in particular) visible.

See attached for a screen shot of that folder.

I see there are a number of conflicted copies of files that must have resulted from sharing issues between these two Macs in the past (which I will be reconfiguring). I've deleted the machine names from the names of each of these conflicted copy files.

I should add that there are no remaining issues with the previous file conflicts (i.e. there are no problems with missing or duplicate messages, etc). So I assume that, besides dealing with the duplicate Inbox, I can also delete all of those conflicted-copy files.

I see there are a number of conflicted copies of files that must have resulted from sharing issues between these two Macs in the past (which I will be reconfiguring).

Then why don't you stop messing with this Dropbox mess, and create a new local profile on each machine? You can then set up the IMAP account in the new profile.

To manually transfer any other existing data, e.g. like the address book, from the existing profile see http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Thunderbird

Thanks. I determined that I didn't really need email on the secondary Mac, so I just deactivated its access to the Thunderbird profile on Dropbox, and will uninstall Thunderbird shortly.

Meanwhile, on the primary Mac, I first made a backup of the Thunderbird profile for safekeeping. Then I searched within the Thunderbird profile for all files that contained the phrase "conflicted copy" in their names, and deleted them. When I restarted Thunderbird on the primary Mac, the duplicate Inbox was gone, and everything else appears normal. So it looks as though it's resolved.