Absolutely normal. Baby acne is a result of their developing sebaceous glands, which were not being used to lubricate the skin while in-utero because they were under water! Some babies have a more visible development then others, basically it takes a few weeks for the glands to become fully active and able to produce the correct amount of oil for their skin. In babies acne is NOT a a sign of allergy unless it occurs after the first few months, and even then it is most likely from a detergent or dander reaction, not a food reaction.
I hear this question a LOT from new moms in my midwifery practice. Keep up the paleo!
Baby acne is really common just from all the hormonal changes going on in them after birth. Mom's diet could be a culprit, but I'd be more inclined to look at the products baby is using for bath time.
"Baby acne" is absolutely normal, and occurs in healthy babies as a normal part of the adjustment to extrauterine life. It is not sickness or inflammation, nor is it something to be worried about or try to "fix". It's caused by the combination of the development of the baby's sebaceous glands (called milia), and a response to the hormones circulating in their body from the pregnancy. Don't pick it, scrub at it, or try to 'heal' it -- it will go away on its own, usually within the first few months after delivery. However, if you pick at it, it can introduce infection and cause scarring.
They probably shouldn't be getting acne in all honestly. Acne is a very obvious sign that there's inflammation in the body and since most of our inflammation comes from what we consume, it's likely the baby is consuming something that it's either genuinely allergic to (not common) or is simply not ready to digest yet (more likely.)