Why should benzalkonium chloride (an antifungal agent) be used during your laundry machine's "rinse" cycle, not its "wash" cycle?
The label of the veterinary product Fung-A-Way, which is Benzalkonium Chloride 0.15%, states that "Efficiency is neutralized by soap or detergent residues."

The website http://www.mpbio.com has the following under its description for Benzalkonium Chloride:
"Incompatible with anionic detergents, such as soap, and with nitrates."