Rye is a grain and the first step to living a Paleo lifestyle is to rid your diet of all grains. Although grains exist on a spectrum, with some being worse than others, rye exists on the end with wheat, which is probably the worst offender.
Paleo and Gluten
Rye only contains a little bit of gluten, but it’s still gluten. Those who are allergic to gluten can’t have rye and the rest of us should probably avoid it as well. Even a little gluten can go a long way to increasing gut permeability and inflammation.
Paleo and Lectins
Rye also contains lectins, another anti-nutrient that has been known to perforate the lining of the stomach and interfere with insulin receptors. This can cause major problems, as insulin is necessary for dealing with the high blood sugar that tends to result from eating grains like rye.
Mark Sisson gave a list of reasons to avoid rye.