I use Ctrl+Shift+V (Paste as Plain Text) extensively overall. However I experienced that in Firefox instead of doing the Paste it opens a sidebar called "Blockable items on current page".
It turned out that this is because of the AdBlockPlus plugin.
To restore the Paste as Plain Text functionality you'll have to
- open the about:config page in Firefox,
- search for the preference name extensions.adblockplus.sidebar_key
- change the value of it to something else than Accel Shift V
- restart Firefox
The solution comes from this source.