Hey @JurgaR,
It’s recommended that you update Cornerstone because eventually it will cause issues in the future due to version incompatibility. But, I just want to clear that the checkbox is not related to Cornerstone as it is included in the theme.
I’ve tested WP 4.9.6 and the default WordPress themes and the only checkbox that WordPress adds out of the box is this: Save my name, email, and website in this browser for the next time I comment..
The rest of the checkboxes in your screenshot are probably added by a third party plugin because if it’s added by WordPress, it will be consistent.
The checkbox that WordPress adds is also available in X and Pro out of the box because they don’t filter the form or are using the standard comment form like the default WordPress themes.
It looks like you have a custom comment form or are filtering the comment form in your child theme. Please switch to the parent theme to quickly know if child theme customization is causing the issue.
To your question on deleting Cornerstone, deactivate and delete it then go to X in your WP Admin menu and the latest version of Cornerstone will be installed automatically for you. Don’t worry about the pages you built with Cornerstone, they will not be affected as the data is stored in the database and Cornerstone does not have a command to delete data upon deletion.
Thanks.