I'm not aware of any built-in way to disable animated favicons/site icons.

One workaround for Adblock Plus users is to block the file using the blockable items list. It's common for site icons to have a .ico extension, but if it doesn't show up that way, I'd try .gif and see whether it shows up under that.

Does that work for you?

That is an advanced setting; image.animation_mode = once

Type about:config<Enter> in the address bar. If a warning screen comes up, press the Be Careful button. This is where Firefox finds information it needs to run. At the top of the screen is a search bar. Type image.animation_mode and change the setting to once.

You can create custom style rules to suppress favicons on tabs of sites that abuse them, but since there's no automatic way to detect animated vs. non-animated icons, this would involve listing the domains as you discover them.

I use the Stylish extension, but this also could be done with userChrome.css if you prefer.

I created a test rule using an annoying site someone mentioned in another thread:

@namespace url(http://www.mozilla.org/keymaster/gatekeeper/there.is.only.xul);
.tabbrowser-tab[image*="annoyingsite.zyx"] .tab-icon-image,
.tabbrowser-tab[image*="universitycoop.com"] .tab-icon-image 
{
  /* These rules remove the image complete and allow the text to use the space */
  display:none !important; 
  width:0 !important;
  margin: 0 !important;
  /* Alternately, these rules hide the image without changing the layout (disable the above if you use these) */
  /*
  opacity:0 !important;
  visibility:hidden !important; 
  */
}

thx for the ideas - I tried "image.animation_mode = once". (I edited it and set "value"=once.) Firefox crashed after restart, but was subsequently ok. The setting was still "once" when I checked, but the undulating obnoxious icon is still undulating.

image.animation_mode doesn't work for favicons, this only works fir GIF images on a web page.

You would have to block this specific favicon or disable (hide) favicons on tabs with code in userChrome.css or disable all website favicons.

• browser.chrome.site_icons = false

This code misuses the throbber to replace a GIF favicon:

@namespace url("http://www.mozilla.org/keymaster/gatekeeper/there.is.only.xul"); /* only needed once */

.tabbrowser-tab[image*=".gif"] .tab-throbber:not([busy]) {
 list-style-image: url("chrome://global/skin/icons/folder-item.png")!important;
 -moz-image-region: rect(0px,16px,16px,0px)!important;
 display:-moz-box!important;
}
.tabbrowser-tab[image*=".gif"] .tab-icon-image {display:none!important;}