Part of living a Paleo lifestyle is avoiding legumes, and peas are, technically, a legume, but there’s more to the story.
Paleo and Phytic Acid
Before we can completely discredit peas, we have to understand why we normally avoid legumes. Well, for one thing, they tend to be high in phytic acid (aka phytates), an anti-nutrient that binds to minerals in the seed and prevents our bodies from absorbing those nutrients. This can often lead to nutrient deficiencies, not to mention inflammation as a result of digestive issues caused by the phytates. The process of sprouting or soaking beans before cooking them can reduce some, but not all, of the phytates.
Paleo and Polyunsaturated Fats
Legumes also tend to be fairly high in Omega-6 fats, a type of polyunsaturated fat that is highly inflammatory. While consuming some Omega-6s is fine, the Standard American Diet (SAD), has increased its Omega-6 content far beyond what our bodies are equipped to handle. Omega-6s are inflammatory and we need to be sure to maintain a healthy ratio of Omega-6 to Omega-3 in our diet. Omega-3s are another type of polyunsaturated fat that have anti-inflammatory properties and help counteract the effects of Omega-6s.
Paleo and Carbohydrates
Although they are protein-rich, legumes also tend to be fairly high in carbohydrates, and living a Paleo lifestyle generally entails limiting carbohydrates and avoiding foods that cause a spike in blood sugar. This is because a spike in blood sugar inevitably leads to a crash, resulting in the continuation of the cycle when your body craves more sugar.
Peas are different because they have been selectively bred (NOT genetically modified!) to be more digestible and palatable. They contain less phytic acid than other legumes, and, unlike beans, cooking peas actually significantly reduces their phytate content (by as much as half).
The sugar content may still be an issue, depending on your personal tolerance. If you do decide to include peas as part of your Paleo lifestyle, go for fresh over dried, as fresh peas tend to be lower in carbohydrates.
Another factor is the portion size. While people tend to fill their burritos with beans, peas are generally consumed only as a side-dish or part of a salad. By eating them this way, you make sure to avoid overloading on phytates and Omega-6 fats.