Can I use non-affiliate link products in the Shop the Post plugin?

No, our Shop the Post plugin is specifically built for WordPress shortcodes or HTML. While you could write your own custom HTML code to load in images of custom selected products, it wouldn't be especially efficient, and would not feature slider progression buttons for users to browse products. 

You can use the Shop the Post plugin to write text-based HTML, so if you are ok with only featuring text-based links (and not worrying about images), it would work for that.