Using the cross sale products in the latest J2commerce version (4.0.12), I realised that all products are loaded regardless of their state. I found out that in $cross_sell_product->source, I can find all article information, so I found a workaround for this for the moment, but I think it's a bug.

Here is my workaround: in the template, in view_crossells.php, find this line:

foreach($this->cross_sells as $cross_sell_product):

and add the following inside the loop:

if($cross_sell_product->source->state !==1) continue;