... the ones that have more polyunsaturated than monounsaturated fats in their msds or their nutrition facts label.
Yep- the ones that are high in polyunsaturated fats are the biggest culprit.
That's not to say one should completely avoid using them in soap formulas, though. Many find they can use them just fine if kept under a certain %. For example, I myself only like to add as much as would keep the total linoleic acid content of my soap from going over 15%.
Some of the most common 'problem' soaping oils where DOS is concerned are canola, cottonseed, grapeseed, hemp, safflower, sunflower, soy. Basically any oil high in linoleic or linolenic acid.