This article doesn't appear to be applicable, as user.js doesn't seem to exist, nor the extension. The article also doesn't explain how to enter the suggested lines in about:config

http://kb.mozillazine.org/Granting_JavaScript_access_to_the_clipboard

Start Firefox using Troubleshoot(Safe) Mode {web link}

A small dialog should appear. Click Start In Troubleshoot(Safe) Mode (not Refresh). Is the problem still there?

The issue still appears to be there.

That said, in normal mode, if I e.g. copy your answer, select this reply box and press Ctrl+V, the copied text gets pasted. If I try the same in another forum, it doesn't and I've to right-click, select Paste and I then get that dialog box as in my original post. It does work if I copy from an external source, e.g. a text editor.

Upon further investigation, I discovered that the forum in question uses CKEditor. So it might be CKEditor's internal configuration which is the cause.

It could be CKEditor if it's a very old or very new version.

Another thing to check is the following preference:

(1) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button accepting the risk.

(2) In the search box in the page, type or paste dom.event.clipboardevents.enabled and pause while the list is filtered

(3) If the has a value of false, double-click it to restore the default value of true

More info on about:config: Configuration Editor for Firefox.