I have been searching for the same, and just ordered the Beauty by Earth facial cleanser. The only 1 in the acne category came from canlendula, which is herb that is anti-inflammatory, anti-bacterial, and anti-fungal. Those all sound like qualities you'd want in an acne fighting product, so I searched for a link between canlendula and acne and apparently it is often used to treat it. I am guessing it's listed as a low factor in the acne category because, as with everything, it could cause a reaction to someone's skin. However, its safe and natural, and since it's the only negative item on the list, I am going to give it a try. I have been using Cetaphil religiously for years, but I still break out frequently no matter what products I use, so maybe using this site as a guide is the answer
You can check it out on their website if you're interested :https://www.beautybyearth.com/product/natural-face-wash/
You can also purchase it on Amazon and read the reviews.
I also ordered their toner and eye cream. I'd be happy to let you know what I think of them once I've used them a few times if you want!