When does WP ignore content added through the backend editor?

It entirely depends on the theme you are using on your site. The default theme will only ignore the content of the blog home page. The reason is:

By default, the blog home page (or when the latest posts is selected as front page) only lists the posts as archives.

However, this behaviour is changeable from the theme. For example, you may customize home.php theme file to change the look & feel of that page or show content added from the backend editor along with recent blog listings. As stated in the WordPress Document:

Do not use a custom Page template for this page. The template files home.php or index.php will be used to generate this page in the Theme.

So as you see, it entirely depends on the theme you are going to use. It’s no way a core WordPress feature & WordPress by itself will neither ignore any content added from the backend editor, nor will it show
them. Depending on your active theme and plugins, they’ll be shown or ignored.

However, as you’ve stated, default WordPress themes generally ignore the page content added from the backend editor from the blog home page. This is the only place it does so & the behaviour is modifiable from themes and plugins, even when you are using any of the default WordPress themes.

Also note that, contents such as category description, post excerpt etc. may also be ignored, however, as it is already stated above, all of these completely depend on the theme you are using (& sometime even the plugins).

You may follow this WordPress document to understand how the theme template files behave & modify your theme behaviour accordingly.