Remove id attribute from stylesheet link

You can filter style_loader_tag. You get the HTML element and the handle as arguments.

Example

add_filter( 'style_loader_tag', function( $html, $handle ) {

    if ( 'custom-stylesheet' !== $handle )
        return $html;

    return str_replace( " id='$handle-css'", '', $html );
}, 10, 2 );

But really, I would not waste processing time for that. The id exists to make the element easier to access per JavaScript. It doesn’t hurt if you don’t need it.