Maybe the reason is that the order of styles and classes in optimized file doesn't match original order of files and css styles. For example, if on page styles and styleshits order is: some file with styles, after that wp_enqueue_script, then some other style, - then the optimized file with css styles should match the original order styles and classes in it's file (styles from first file at the beginning, then styles from wp_enqueue_script, then other styles, etc.).
And why the problem doesn't appear on website when admin account is used..?