How can I style the WYSIWYG content? Let's say I'm currently editing a page and there is a WYSIWYG editor in the backend to edit a specific part.

Now I add a table via the WYSIWYG. How can I apply CSS styles on that table WITHOUT altering the CKEditor plugin settings (I don't want to provide classes in the "Styles" dropdown)?
You can either implement hook_ckeditor_css_alter or you can add ckeditor_stylesheets to your themes info.yml file.

See: hook_ckeditor_css_alter for more.

Example:

function mymodule_ckeditor_css_alter(array &amp;$css, Editor $editor) {
  $css[] = drupal_get_path('theme', 'mytheme') . '/css/mymodule-ckeditor.css';
}


Or in mytheme.info.yml:

ckeditor_stylesheets:
  - css/styles.css