The add-on I mentioned was off-topic and was not intended to suggest was the cause of your issue simply because the "Upgrade your browser..." message is not an "ad" but is instead an error message produced from Yahoo in the event that Yahoo "thinks" (right or wrong) that the browser you're using is not up to date. Sorry if my "off-topic" comment caused any confusion, so then you're already using that extension.
OK at this point you could try the following steps:
1) Type in your FF address bar, "
about:config" (without the quotes) and press
Enter (like typing a site address).
2) Ignore the warning by clicking on "I'll be careful, I promise!".
3) In the "Search" filter type "
general.useragent" without the quotes (you should see the same as what you see in the image below, if so you can skip the next step #4 below).
4) If any of the three preferences are displayed in
BOLD characters then it is a "user set" preference so in that case
right-click on those that are displayed in
BOLD and select "
Reset" from the context menu (if the settings are already set to "default" [non are BOLD] then the "Reset" in the right-click context menu will be disabled [grayed out]).
In the end you should see the following preference settings in your about:config:

- about config settings re useragent.png (10.02 KiB) Viewed 13104 times
If you have the above set as displayed and your problem persists then since you are using the current version of FF (version 39), I'm sorry to say that I'm frankly at a loss as to why Yahoo is behaving the way it is other than to say it would appear to be some kind of "glitch" in Yahoo (that apparently doesn't appear to be currently impacting anyone else that I'm aware of).
As I posted previously, I'm presuming that you're getting this "Upgrade your browser..." message in the Yahoo Email Client itself, that is when logging into your Yahoo email account(s) directly on the web using your FF browser.
Since this is what occurs using FF then if you have any other browser(s) i.e. Internet Explorer (IE) you could try using this browser instead of FF just to see if this makes a difference when logging into the Yahoo Email Client on the web. If another browser does not have this problem then for now you could either set the browser that works as your default browser for now to avoid this issue until the problem can be resolved (
Jeff will hopefully have some other ideas or suggestion) or for lack of any other option since in the event at this point another browser does not have the problem and FF does then as a last resort you could (at your own risk) optionally take a look at this FF link:
https://support.mozilla.org/en-US/kb/re ... references" onclick="window.open(this.href);return false; or you could go so far as to re-install Firefox, before you do this however you should copy your profile folder(a folder with some unique name) in some other location of your hard disk then after reinstalling firefox, copy and paste this folder back in same location (location: %APPDATA%\Mozilla\Firefox\Profiles\).
Word of warning, I'm not familiar with these instructions from Firefox posted in this paragraph (as I haven't done any of this myself) and therefore do not vouch for them as a way to solve your problem. With that in mind,
it may be ADVISABLE TO WAIT AND SEE IF JEFF CAN COME UP WITH ANY OTHER IDEAS regarding your problems if at this point your problem persists.
Let us know if your problem is eventually solved at some point, if not we'll get back to you when we can come up with any further ideas on what can be tried to address this issue.