It is the Safari Update that broke it, not Mojave. I am still on High Sierra and the Safari update broke it.
This is a workaround - it works but is a bit fiddly and you have to re-run the Extension every time you launch Safari:
1. Download the extension, eg. Pinboard "Save All Tabs"
2. Change the file extension from .safariextz to zip.
3. Extract files.
4. Click "Show Extension Builder" in Safari Develop menu.
5. On the lower left corner there is a plus button.
6. Click it.
7. Choose "Add Extension".
8. When you get asked to, open the folder where you have saved the extracted files of your extension .
9. Click "Run" in the upper right corner of Extension Builder.
10. You will have to re-run the extension every time you launch Safari.
10.1 After relaunching Safari, open Develop Menu.
10.2 Click "Show Extension Builder".
10.3 Click "Run" in the upper right corner of Extension Builder.
IMPORTANT:
Keep your "Extension folder" in same place on your Mac.
Do NOT delete the Extension File.
(I made a new "Safari Extensions" sub-directory in my Applications Folder so I can find them easily.)
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Thank you to StellarVixen on Mac Rumours for that tip:
Best wishes,
Liz