The Mozilla browsers which include Firefox has supported 256-bit even encryption for a long time now so it yes it supports 128-bit.

The issue could perhaps be the site is looking for the old obsolete U in the useragent which was used to specify the encryption strength of 128-bit though 256-bit has been supported for a long while already at time by Mozilla applications. This "U" was removed in Firefox useragent as of 4.0 which was released March 22nd, 2011.

http://en.wikipedia.org/wiki/User_agent#Encryption_strength_notations https://hacks.mozilla.org/2010/09/final-user-agent-string-for-firefox-4/

Actually 128 bit encryption is outdated and shouldn't be used these days. 256 bit encryption should be standard for any site that wants to be safe. There is usually a button to continue if you get redirected to a page that test if you meet the requirements. It shouldn't pose a problem to continue in cases like that.

128 bit encryption is outdated

AES 128-bit encryption is not outdated by any means.

and shouldn't be used these days.

Who says that?