...Since preservatives are pH specific, formulated for lotions and creams and like products, and since there is no preservative specifically formulated for liquid soap...
Preservatives are chemical blends that have certain requirements (pH, temperature, presence or absence of other chemicals, etc.) to function properly. If your particular product contains ingredients or other properties that do not meet the requirements, the product is incompatible with the preservative. It doesn't matter whether the product is lotion or soap.
There are 3 preservatives I know of that are suitable for alkaline products, which includes liquid soap -- Liquid germall plus (to pH 10), Phenoxyethanol (to pH 10), and Suttocide A (to pH 12).
"...would it be safe to say that as long as your LS is pH 9 to 11, no preservative is necessary?
No, I don't think it's safe or even reasonable to say that. It makes no logical sense. There
are preservatives suitable for alkaline products. Ergo, there
are preservatives suitable for liquid soap should the maker decide to use a preservative.
Even if there were zero preservatives that were effective at the alkaline pH of liquid soap ... that would
still not prove your point that preservatives for LS are unnecessary.
"...As to the point about adding water to liquid soap, I just tested the LS in my foamer... It has a pH 9.5 and no sign of nasties or mold..."
Last time you got food poisoning from eating contaminated food, did you see, smell, or taste the E coli, staph, clostridium, norovirus organisms in the food? It is a scientific fact that just because you can't SEE microorganisms growing doesn't mean they aren't present in numbers that may be a health hazard.
I do not understand why you persist in believing contaminated B&B products have to show visible signs of microbial growth before you deem them contaminated. It makes no sense to have that point of view.
Some of us are going to use preservatives in liquid soap and some of us won't. I'm pretty careful in my comments about the preservative vs. no preservative wrangle to leave room for a variety of opinions. There's no need to bolster your no-preservative point of view with pseudo-scientific logic. Whether you do or don't makes no matter to me -- I will be the last one to lecture you that you should add preservative.
***
For those who are reading this and wondering what my advice is -- The more dilute the liquid soap, the less stable the alkaline pH will be in the long run. The more food sources people add to liquid soap, the more likely that microbes are likely to grow. For both of those reasons, using a preservative may be a wise choice. If you add more than a trace of microbial food (aloe, milk, sugar, honey, etc.) to liquid soap, it's very likely
no preservative will be effective, including the preservative effect of high pH. If you choose use a preservative, use one that's rated for the alkaline pH of this product and also keep the food content in your liquid soap very low.