Thanks BruceG and thanks to SoundFoundation too.
My problem was also being caused by SIMBL.osax in Scripting Additions. Pulling out just that one file cured the problem. The only other item in the folder is Glims.osax which I did not investigate. Neither did I investigate any of the items in Internet Plug-Ins.
SIMBL.osax is a hack to allow other software to run. In my case, it had been installed by AdBlock (an extension for Safari).
I had SIMBL 0.9.7 installed. I went to http://www.culater.net/software/SIMBL/SIMBL.php and downloaded the latest version (0.9.9). First I ran the uninstaller to get rid of any old stuff. Then I tried installing 0.9.9. Running Safari again showed that the blank Privacy or Extensions tab problem had returned.
I have now uninstalled SIMBL and AdBlock too (as it wouldn't work without it). All is now fine.
Update/correction to my previous post...
It looks like I must have previously had a different ad blocking program installed. After consulting with the author of AdBlock For Safari it is now clear that it was not his Adblock that was responsible for getting SIMBL into my system. AdBlock For Safari is an extension and so does not require a helper plugin like SIMBL to function.
Be aware, there are several ad blocking products around with similar names.
SIMBL removed, AdBlock For Safari is running just fine.
Get it here: http://safariadblock.com/