Are allergies genetic?

Yes: Allergy has a significant element of genetics. It is not caused by a single gene. There are also multiple influences by the environment. Children where parents who have allergies are nearly certain to suffer from allergies. If only one parent has allergies, less than half will have allergies on the average.

A genetic component: any of the triad of allergies, eczema, and asthma frequently "run in families", so there clearly is a genetic component. A given individual in the family may either inherit the predisposition, or will not. Other factors are now becoming known for children developing allergies. Breast-feeding significantly decreases the risk, as does allowing the developing child to "play in the dirt".