Food Offered to Idols
My first read of this made no sense, I had no idea what it was talking about. I googled around a bit and found this page which explained that in pagan rituals they offer food to idols and some of the food gets eaten by the people attending the ritual.
If you eat food offered to the idols, it will not change anything, it won't make you better or worse because the Gods of those idols don't really exist and therefore have no real power. However, if someone who else sees you eating that food they might think that the other God's exist. This would cause an indirect harm and therefore you should not eat that food.
This seems pretty reasonable from their perspective. It won't really do anything because those Gods are fake so giving them attention is bad. From a marketing perspective it is really good, it's not exactly condemning the other religion, but it is keeping your people from standing in both camps.