I would't say it was that much of a problem.
It strikes me that if this scrap is sorted magnetically by dipping an electromagnet on a crane into it, it's a fair bet that the majority of the scrap collected in this way will be either iron or steel.
When this magnetic scrap is put into the furnace, the wood, plastic and other stuff is burnt off immediately by the intense heat. It follows that If the furnace is at the right temperature for melting iron or steel, the furnace should now only contain iron or steel. Other "impurities" are also probably floated off as slag.