GDM does not update a user group membership on logout/login

[spacebug]

I'm running GNOME in Debian Stretch. This uses GDM by default.

If I want to add my user to new groups (for example sudo) I run

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adduser <myuser> sudo

in a console.

After this I can typ

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id <myuser>

and see that I have been added to the groups.

But only typing

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id

does not show the new membership. (This is because you have to logout and in again to update the membership for any shell).
The thing is, this does not work with GDM!
Logout and in again does not show the new group membership when issuing command

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id

I have tried restarting GDM.
I have also tried completely killing GDM and starting it again.
Nothing works. The only thing that really works is to reboot the computer.

I have not tried any other login managers so I don't know if this is a design bug/miss or maybe only a but in GDM.

[bryanmc]

Why not # usermod -aG sudo <username>