How to save a checkbox config_object in the schema files?
You are creating your checkbox options as an associative array of node type (bundle) IDs as keys and their labels as values.

When this form is submitted, checked checkboxes submit as key =&gt; key. So the stored information (I suppose 'rss_url' in your question is intended to being 'mymodule_enabled_content_types') is similar to:

mymodule_enabled_content_types:
  article: article
  page: page
  custom: custom


As the keys of the submitted values are unknown before submission, and the values clearly are strings, this is a sequence of strings (compare https://www.drupal.org/docs/8/api/configuration-api/configuration-schemametadata#properties). The correct schema definition is:

mymodule.settings:
  type: config_object
  label: 'My Module settings'
  mapping: 
    mymodule_enabled_content_types:
      type: sequence
      label: 'Enabled Content types'
      sequence:
        type: string


After changing your schema definition and rebuilding your caches, your form submit handler should work just fine and the configuration being saved using its correct data types.