I actually do not see a way to turn off that feature for either regular or pinned tabs.

One idea... You may have noticed from time to time that Firefox asks whether you really want to close a tab or leave a page. Sometimes it's helpful, to prevent losing work, while other times, it's to try to prevent you from leaving an annoying page. I mention this because it would be possible for an add-on to set up that feature for pinned tabs to prevent accidental closure, but of course, it would also require an extra click to close them.

Thanks for the reply. I wouldn't mind the 'extra click' to close a pinned tab, but urgently want to prevent a mistaken-middle-click close.

I didn't see an add-on for this, so as a temporary workaround, you could use a bookmarklet to inject a script into each pinned tab you want to protect against closure. Note that this script lives in the current page, so you would need to repeat the exercise after navigating to a new page. Here's how to set it up:

(1) Copy the following script:

javascript:void(window.addEventListener('beforeunload', function(evt){evt.preventDefault();}, false));

(2) Right-click a convenient part of the Bookmarks Toolbar > Add Bookmark

(3) Assign a short title like NoClose

(4) Paste the script into the URL

(5) Click Save

Now when you are on a page you don't want to easily close, you can click the bookmark to inject the script.