I read the ingredients list on the website. One item was "disinfectants" which doesn't actually give you any information. I'd want to know exactly what those are. I didn't check the chemicals listed, but they seem to be the same or similar to those found in Lysol.
AFAIK, the problem with anti-bacterial cleansers is what's used to kill the bacteria. If a cleaner uses chemicals like Lysol uses or chemical like lactic acid, H2O2, bleach, alcohol, etc., that's fine. The problem is when an anti-biotic such as Triclosan (common in the U.S.) is used. This is fuel added to the fire of anti-biotic resistance.
On the one hand, my gut tells me that if having bacteria-free laundry were important, there wouldn't be 7 billion people on the planet. On the other, maybe the epidemic of cold water washing changes that.
Also, from a public health standpoint, I'd think it more beneficial to have a detergent that killed moulds and virii
Jim