Bookstagram - Excluding a Category from Featured Posts
There isn't an option in the Customizer to exclude a category from the featured posts area. You can limit it to only show a certain category, but you can't show all except one category.
The only way to do this is with custom code. You need to create a child theme and place this snippet in your child theme's functions.php file: https://gist.github.com/nosegraze/7e46ba74c1bea5f699dad6ff66d722df
Note that the featured posts results are cached and only update when the Customizer settings are saved or when a new post is published. So you won't see your changes immediately. You have to either re-save the Customizer settings or wait until you publish a new post.