I visit very often GNU/OpenSource websites like debian.org, and I’ve never seen there pictures in GIF format.
Why there are no GIFs on GNU Web Pages?

And of course, I found an answer on gnu.org:
There are no GIFs on the GNU web site because of the existing GIF patents Unisys and IBM covering the LZW compression algorithm which is used in making GIF files. These patents make it impossible to have free software to generate proper GIFs. They also apply to the compress program, which is why GNU does not use it or its format.

Unisys and IBM both applied for patents in 1983.

The Unisys patent expired on 20 June 2003 in the USA, in Europe it expired on 18 June 2004, in Japan the patent expired on 20 June 2004 and in Canada it expired on 7 July 2004. The U.S. IBM patent expired 11 August 2006, The Software Freedom Law Center says that after 1 October 2006, there will be no significant patent claims interfering with employment of the GIF format.