Rancidity and oxidation are two different things. A fat can be rancid or oxidized or both. Oxidation is the breakdown of fat into diglycerides, monoglycerides, fatty acids, and glycerin. Rancidity is the breakdown of fats and fatty acids into ketones and aldehydes, which are the chemicals that give rancid fat that distinctive "off" odor. See the difference?
Further, the issue of rancidity in soap is not quite so cut and dried. Using rancid fats certainly leads to soap that is rancid, but you can get rancidity in soap even if you use fats that test perfectly fresh.
Spots of rancidity (DOS), such as Loriag is seeing, come from discrete contaminants, most likely metals that come from harvesting and processing machinery, soaping equipment, the air or one's hands, etc.
Overall rancidity can be created by rancid fat, but it can also be triggered by other ingredients that are mixed throughout the soap. Examples include oxidized essential oils (older lavender EO being a prime example), or metals in tap water, or additives that supply metal ions; chlorophyll being one culprit.
You can do your best to minimize the chance of overall rancidity or DOS, but you can never entirely eliminate the possibility. You can also use additives to combat oxidation and rancidity if and when it happens. These include chelants, such as tetrasodium EDTA and citrate, and antioxidants, such as rosemary oleoresin (ROE). Pairing a chelant with an antioxidant is a good way to go -- EDTA pairs well with ROE, for example.
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