There is evidence that children born via C-section have more asthma and allergies.

No, their immune system should be normal for age.

There is some truth to that, but it turns out that C section babies are more prone to developing atopy in childhood and adulthood. The important factor is what skin flora colonizes the baby's GI tract: skin flora from the nurses, the caregivers and the mother OR the mother's birth canal. I recommend you read up on the role of the microbiome in C section babies. Some OB/GYNs are now using what is called a "seeding" procedure. Hope this information helps.