Some of my products are appearing in my store and shouldn't be. They are set to visibility none and visibility internal. Why can shoppers still see them?
Most likely you have the category link elevation box checked in the top level category or subcategory for the product. The Category Link Elevation option allows you to grant visibility to the category to any customer who enters the Online Store via the Category Link (displayed on the Category Detail screen), regardless of the value of the Visibility field.
When Category Link Elevation is activated, the elevation applies to all products in the category, in addition to the category itself. If the category has subcategories, the elevation applies to those subcategories and their products, recursively down to the bottom category level. If the category has a parent, the elevation applies to the parent, recursively up to the top level, to maintain the category path intact. To hide those products, find the culprit category(s) and unclick the box.