That bottom panel is from the “Window List” plugin.
And Gnome 3 classic uses it as a required plugin and ignores user settings even if it is disabled.
A dirty fix is to just remove the directory for the plugin:
If you want it back later, you may re-install that plugin’s package.
# yum reinstall gnome-shell-extension-window-list
Hover over a blank part of the bottom panel. Press
Super + Right Click. Press delete/remove this panel.
Nice trick! Please also note that this is available only after certain version of Gnome 3 classic (I am not aware of which though).