My fault, I wasn´t precise enough with investigating.
I uploaded all files again and re-initialized the templates with no effect.
Then I found out, why only one user is showing up with the avatar. This user has an avatar from our regular avatar-database, not a customized one.
So the gallery-soft obviously can´t find the path to the customized avatar-uploads.
-- Edit ---
Meanwhile I found this thread Custom Avatars not loading
and according to it I checked my customavatar-path-settings, which were correct.
But the custom-avatars in our forum are stored within the database itself. Maybe I should move them to the file-system (according to the ACP-option) to let the gallery find them finally?