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GTK is the Gimp ToolKit originally, predating GNOME as far as I know.

GTK came from the Gimp, not Gnome.

Okay, but even if GTK is a GNU project or a FSF project, why does that mean it qualifies for being part of a future GPLv4 licensed EMACS, and QT does not? Both are available under the LGPL. I wonder if Stallman expects that a GPLv4 would likely or definitely be incompatible with LGPL3. I don't think it's because the LGPL version would be bumped if a v4 came out; GTK is still on LGPLv2.1

It is because of the license. GTK's license is LGPLv2.1 or later[0]. The important part is later, It means you can update it automatically to any later version, especially if the new license is not compatible with the previous version. Qt does not offer their software with a similar license.

[0]: https://gitlab.gnome.org/GNOME/gtk/-/tree/master#licensing-t...