I had the same problem since 1.9.25.
You can temporarily fix the problem on your own by changing /wp-content/plugins/nextcellent-gallery-nextgen-legacy/widgets/class-ngg-gallery-widget.php in line 53 from
} elseif ( $new_instance['allow'] ) {
to
} elseif ( $new_instance['exclude'] == 'allow' ) {
I hope the plugin’s developer will put this fix in next version.
