Use this hook to determine if a field should appear in the WooCommerce cart and the email confirmation from WooCommerce. Replace 123, 345, and 456 with the field IDs you want to show. Replace 987, 765, and 543 with the field IDs you want to remove from the cart.

add_filter( 'wc_fp_include_field_in_cart', 'frm_show_field_in_cart', 10, 3 );
function frm_show_field_in_cart( $display, $field, $value ) {
    if ( in_array( $field->id, array( '123', '345', '456' ) ) ) {
        $display = true;
    } else if ( in_array( $field->id, array( '987', '765', '543' ) ) ) {
        $display = false;
    }

    return $display;
}