Remember that gods are real and active in the setting. If "no incest" is a command from a god that can actually smite you then there's much more incentive to listen.
It wasn't explored that much but the problem seems most likely to be about the genetics since they don't see a problem with one whole family of women being married or at least in a relationship with a single man and not regarding adopted siblings as incest. Furthermore the exact nature of the crime wasn't incest but "father desiring his own daughter". With the curse there's already going to be lots of problems with the gene pool, most people will be cousins or only slightly removed. In that situation direct father daughter or mother son couplings would exasperate the problem fast.
Personally I just assume that in lore Ishtar, who seems to know at least something about the curse since she can shield her priestesses first child from it, gave a divine commandment against parent-child and possibly direct sibling relationships specifically.