Let's try to do a refresh, then we'll try to use the built in updater like before!

The Refresh feature (called "Reset" in older Firefox versions) can fix many issues by restoring Firefox to its factory default state while saving your bookmarks, history, passwords, cookies, and other essential information.

Note: When you use this feature, you will lose any extensions, toolbar customizations, and some preferences. See the Refresh Firefox - reset add-ons and settings article for more information.

To Refresh Firefox:

1. Open the Troubleshooting Information page using one of these methods:
   • Click the menu button , click help and select Troubleshooting Information. A new tab containing your troubleshooting information should open.
   • If you're unable to access the Help menu, type about:support in your address bar to bring up the Troubleshooting Information page.
2. At the top right corner of the page, you should see a button that says "Refresh Firefox" ("Reset Firefox" in older Firefox versions). Click on it.
3. Firefox will close. After the refresh process is completed, Firefox will show a window with the information that is imported.
4. Click Finish and Firefox will reopen.

Did this fix the problem? Please report back to us!

Thank you.

I'd certainly try that but I can't start Firefox in order to do so, unless there's some even-more-safe-than-safe-mode way of starting it.

Can we try a clean reinstall then?

Certain Firefox problems can be solved by performing a Clean reinstall. This means you remove your Firefox program files and then reinstall Firefox. This process does not remove your Firefox profile data (such as bookmarks and passwords), since that information is stored in a different location.

To do a clean reinstall of Firefox, please follow these steps: Note: You might want to print these steps or view them in another browser.

1. Download the latest Desktop version of Firefox from mozilla.org (or choose the download for your operating system and language from this page) and save the setup file to your computer.
2. After the download finishes, close all Firefox windows (or open the Firefox menu and click the close button ).
3. Delete the Firefox installation folder, which is located in one of these locations, by default:
   • Windows:
     • C:\Program Files\Mozilla Firefox
     • C:\Program Files (x86)\Mozilla Firefox
   • Mac: Delete Firefox from the Applications folder.
   • Linux: If you installed Firefox with the distro-based package manager, you should use the same way to uninstall it - see Install Firefox on Linux. If you downloaded and installed the binary package from the Firefox download page, simply remove the folder firefox in your home directory.
4. Now, go ahead and reinstall Firefox:
   1. Double-click the downloaded installation file and go through the steps of the installation wizard.
   2. Once the wizard is finished, choose to directly open Firefox after clicking the Finish button.

More information about reinstalling Firefox can be found here.

WARNING: Do not use a third party uninstaller as part of this process. Doing so could permanently delete your Firefox profile data, including but not limited to, extensions, cache, cookies, bookmarks, personal settings and saved passwords. These cannot be easily recovered unless they have been backed up to an external device! See Back up and restore information in Firefox profiles.

Please report back to say if this helped you!

Thank you.

Yes, I tried that already (see in my original question: " - download and install a fresh Firefox 58.0 DMG; - start that fresh 58.0 in safe mode."). Installing Firefox 58.0 from the DMG involves dragging it to Applications, which prompts whether to "Keep Both" or "Replace"; I choose "Replace" which deletes the old Firefox app package from Applications.

Then that means your FF didn't install correctly if you getting that message. Previous FF wasn't uninstalled. So you need to go back and find all FF install and uninstall them first. I found for FF never choose replace but uninstall it completely then fresh install will prevent any bad or corrupt files from messing up the install.

You are mistaken; removing /Applications/Firefox completely does not improve things. Still fails, in identical ways, whether I install 58.0, 59.0b3, 60.0-a1, or 57.0.4.