I have decided that for all pages where multiple posts are shown (e.g. front, category, tag pages), that post images should not be shown. Instead, featured images, if specified, should be shown next to each post.
Right now, featured images are working fine for posts. However, when multiple posts are displayed (e.g. on the front page, category pages), images should be stripped from the posts.
When a single post is displayed, the images should display as well.
I'm assuming that this has something to do with add_filter() and a regex str_replace() on the post, but this would affect the post no matter where it's displayed.