No, Dr. B probably uses Vit E as an antioxidant in the oils BEFORE making soap with it. I went to their site and copied a list of ingredients for you:
https://www.drbronner.com/DBMS/BABYMILD/OLBA02.html
Water, Organic Coconut Oil*, Potassium Hydroxide**, Organic Olive Oil*, Organic Hemp Oil, Organic Jojoba Oil, Citric Acid, Tocopherol
Please note that there is no preservative in there. And before you think that the citric acid is being used as a preservative, it is not. They almost certainly make lye heavy soap(for clarity), then pH balance with a citric acid solution to bring it down to a safe pH level. There is also the distinct possibility that they are adding Vit E as strictly "label appeal".
If you are selling the soap, then you need to go by what a safety assessor says. There really is no need unless you are adding ingredients(such as anything sugary) during dilution that will provide a better medium for bacterial/fungal growth. This is why we say to dilute with water only. The pH is just too high for any pathogens to survive.
If you are that concerned about your soap growing "stuff", how about just diluting what you need from paste as you need it? I routinely store paste and dilute as I need it. I keep my paste in the fridge, not that I need to, but I won't lose it if it is there. I just put the cooled paste into a Ziploc bag with the name, date, and dilution rate written right on it. That way there is no guessing what it is.
I am also going to reiterate what Craig said. If you have not been making liquid soap for a while, you are not ready to sell. There are so very many different recipes to try to see what you like best, that you won't know if you are selling your "very best" until you have tried many batches on friends and family.
I don't think it will take a year like bar soap does, but if you are still this worried about preservatives, longer than this. Because if you will make some soap, label it with name and date made, and set it aside, you will see that it does not grow stuff for yourself. Then you will not be worried about preservatives any longer.