Viström

Vistrom Media Library Categories provides the ability to categorize and filter your files in the WordPress media library. You can use it in the grid view, list view and in the media modal. The plugin also provides bulk actions to add or remove categories for multiple attachments at once.
<h3>Features</h3>
<ul>
<li>Use any taxonomy for attachments (built-in or custom)</li>
<li>Assign the terms in media library or the regular list view.</li>
<li>Filter attachments by terms in media library and admin-list.</li>
<li>Bulk edit attachments in either the media library or admin-list.</li>
</ul>

Viström Media Library Categories

Categorize and filter your media library by categories, added support for bulk editing in both list-view and the grid-view.

MasterNs

Bulk post editing allows you to apply actions on a number of selected WordPress posts instead of doing it manually on each post 
which could be time consuming particularly if you have a large amount of posts.
However, default bulk editor allows you just to add Categories to Posts. 
This plugin extends default Bulk Editor so you can remove Categories from posts.
The plugin works with default Post type, Woocommerce products and any other Custom Post Type. Supports multiple taxonomies per post.

Bulk remove posts from category

Simple and very good

Not working

Now you can use default WordPress Bulk Editor not just to add Categories but also to remove categories from posts.

Viström Media Library Categories vs Bulk remove posts from category