How can I avoid this markup is filtered out from my block?
I've had the same issue with CKEditor removing classes in the past, Full HTML is not the issue.

Add the below code to the end of your CKEditors config.js file, which is found within the CKEditor library code.

CKEDITOR.config.allowedContent = true;


You might find that the file is called ckeditor.config.js and that this is the file that needs to be changed rather than the default config.js. This file can be found in the root of the CKEditor module.