Use responsive images inline I can see that using styles on inline images have been left out for some reason. But when I need to make the site behave a little more responsive. 

I have been looking after CKeditor plugins that could select a style for the image being include. But I haven't found any. 

I have been looking after at comment on the Drupal 7 Picture module that should be what is the base for the implementation of Responsive Images in Drupal 8. But there is nothing about inline images to find - just old Drupal 7 demos on how it should work.

Any idea how to get responsive images or just a basic image style for images include in inline editor on Drupal 8?
The module Entity Embed will be able to do that. There is now a dev version available, but you better wait for the first alpha/beta-release.

Even longer it will take, until this is in core:

Allow image style/responsive image mapping to be selected in Text Editor's image dialog

This is postponed to drupal 8.1

Until then you can use jquery to move the image from an image field to an empty container in the body. To avoid flicker effects, add a style display:none in the twig template of that specific image field and show it after moving it into the body in jquery.