Search extensions from addons.mozilla.org can't be installed

This seems to be a bug in the Ubuntu version of Firefox -- started with a Mozilla ticket here https://bugzilla.mozilla.org/show_bug.cgi?id=1166508

The short version is that search extensions from addons.mozilla.org fail to install with the error "Sorry, you need a Mozilla-based browser (such as Firefox) to install a search plugin." This can be observed either by navigating directly to, e.g., https://addons.mozilla.org/en-US/firefox/addon/wolfram-alpha-searchextension/ OR by going to Preferences | Search | Add more search engines... in the Firefox menu.

I just got a chance to try this immediately after a fresh install of 14.04.3 x64 desktop, fresh /home and everything, and got the same error. So, it seems to clearly be an Ubuntu bug. However, deleting the preinstalled plugins in /usr/lib/mozilla/plugins/ doesn't work around the issue. The only thing that does is restarting in safe mode (via the Firefox help menu).