This is reviewed in a recent paper. Though not inherited in a simple Mendelian fashion it is a disease of genetic predisposition. This results in considerable overlap with atopic conditions. Some key points:
EoE is a complex genetic disease. Five susceptibility loci have been identified to date.
Three of the EoE predisposition loci are shared across other atopic phenotypes; the remaining two appear to be specific to EoE
The effect sizes of the shared loci are more significant in EoE which may facilitate the characterization of the loci and development of novel therapy.