Prevent installation of style.css cookies and file caching

I expect that your theme has code similar to this in it:

wp_enqueue_style( 'themename-style', get_stylesheet_uri() );

You need to alter this to have version information, like so:

wp_enqueue_style( 'themename-style', get_stylesheet_uri(), array(), '1.0' );

Where “1.0” is the version of the theme.

Now, every time you alter that stylesheet, you need to update the version number. This updates the URL to have the new version, and thus busts the cache.