Is there a way to enable Cross-Origin Resource Sharing for WordPress’ ajaxurl?

Milo is correct.

For instance, go to your theme’s functions.php file, and add the following:

add_filter( 'allowed_http_origins', 'add_allowed_origins' );
function add_allowed_origins( $origins ) {
    $origins[] = 'https://site1.example.com';
    $origins[] = 'https://site2.example.com';
    return $origins;
}

Now an ajax call from https://site1.example.com to your site’s ajax url will have the appropriate Access-Control-Allow-Origin header in the response. eg.

$.ajax({
    url: 'https://site1.example.com/wp-admin/admin-ajax.php',
    type: "POST",
    data: {
        ...
    },
    success: function(doc) {
        ...
    }
});