I have solved my issue (which seems to have been a couple of problems).
Fritzing on macOS stores data in a number of locations:-
1. Within Fritzing.app /Applications/Fritzing.app/Contents/MacOS/fritzing-parts
2. User files, typically ~/Documents/Fritzing
3. Configuration files ~/Library/Preferences/org.fritzing.Fritzing.plist
4. ~/.config/Fritzing/backup
There seemed to be a number of issues:-
1. .config/Fritzing only seemed to contain very old files from an old version of Fritzing, so I deleted it.
2. ~/Documents/Fritzing seemed to have 2 parts lists, viz. my_parts.fzb My Parts.fzb
3. When I deleted and reinstalled Fritzing I had 2 MINE parts, and was unable to delete either, and still was unable to update.
I backed up, then deleted ~/Documents/Fritzing ~/Library/Preferences/org.fritzing.Fritzing.plist
I reinstalled Fritzing (yet again) and it worked, and updated OK. I had to manually set Preferences.
I gradually restored all my User files, manually combined parts into my_parts.fzb and it now appears to be operational.