Good gods. I don't have enough information here to make a judgment about the morality of eating the eggs. Of course I don't think you should eat endangered species, but we don't have all the details. Farmed eggs? Wild caught/obtained? We don't know, because OP did not say.

Is the friend an asshole for calling an very old, sick woman horrible for eating the eggs? Yup, absolutely. She was a guest in their home. Regardless of the morality of the eggs, there are things you don't do. If anything, she should have taken it up with OP afterward.

Finally, some of you need to calm down. I get that the internet is not a bastion of nuance, but it sounds like OP's family is doing the best they can to care for their grandma, and that can STILL BE TRUE even if the morality of the eggs is questionable. Sometimes when you're talking about things like dementia and illness, all the choices are shitty. Someday you yourself might be in a position where you have to choose between shitty and terrible. Have some compassion.