How to disable colored emoji font in Firefox?

It's not installed as a system font. The font file is contained within the Firefox directory, and deleting that one is sufficient. Note that you'll need to actually delete or move the file - simply renaming it, even changing the file extension, is not enough to prevent its use.

In the current Aurora build, the file you'll want to remove is <firefox>\fonts\EmojiOneMozilla.ttf, where <firefox> is the installation folder, which will vary depending on the bit-ness (Program Files or Program Files (x86)) and channel (Mozilla Firefox, Aurora or Nightly). On Windows you can right-click Firefox shortcut and select Open file location.

See also: https://bugzilla.mozilla.org/show_bug.cgi?id=1231701#c135

Go to about:config, context menu (right click) > new > string. Set font.name-list.serif.x-unicode as preference name and Segoe UI Symbol as string value.
Colored emojis are instantaneously disabled, no need to refresh open tabs or restart the browser.

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