Take your daughter with you to the grocery store. Tell her that her friend, we'll call her "Peggy" really likes the breakfast cereal that your family buys, and tell your daughter that she'll have to buy this week's supply. It's amazing what happens when your kids are forced to buy stuff. My son needed another backpack one time, and I was sick of buying expensive backpacks that got ruined quickly. So I took him with me and told him to choose one. Of course, he chose the top of the line backpack with all the extras. I said, fine. He looked at me with both surprise and suspicion. Then I told him that it would come out of his allowances for the next several months, or he could pay for it outright then and there. Wow, his standards changed instantly! He found an inexpensive but perfectly good one and said "actually, this is all I need, really". So I suggest to you that you make your daughter contribute to the groceries and tell her that really, it's Peggy that's taking a big bite (pun intended) out of the food budget. Ask your daughter if she would be ok with this if this situation were taking place in her own apartment, with her own groceries that she bought and paid for with her own income.
And no, people don't do this. It's not you. This is rude. This is your home, "Peggy" is not your friend or the daughter of your dear friend, and I don't think you should hesitate to politely, respectfully and calmly tell Peggy that she may not have eggs unless she tends to the chickens and buys feed for them, and she may not help herself to food that is not set out expressly for guests. If it's in a cupboard or the fridge, it's off-limits. Stand your ground but do so with great kindness and in no uncertain terms.
I have experienced two similar situations. One involved a friend of my daughter's who decided that not only would he eat nothing but garden salads, he would also loudly preach and criticize and mock anyone who ate grains, protein or anything else. I'm sure it was a brief phase but it was so annoying and rude and it ruined every time the kids got together for homework or video games or anything. I told him he could come over, but could not be the food police in our home. He chose not to return.
The other situation was a kid who berated my daughter, mocked her, and made fun of her and accused her of making up her medical diagnoses (she has several of those so-called "invisible" disorders). But he followed other neighborhood kids into the house and he was hungry and neglected in his own house by a drunk, abusive mother. He even told the other kids that I was "lame" because I couldn't curse like his mom. He was pretty desperate for love and attention. I told him, in no uncertain terms, that he could come into our home, but his language and behavior had to be 100% polite and respectful. He chose food and a pleasant home over bad behavior and when he came into our home after that, he cleaned up his language and abided by my rules.
I think you need to demonstrate to your daughter how boundaries are established and how to politely demand respect for people's belongings. Otherwise, when your daughter has her own place, she's going to be pretty miserable. I think your daughter doesn't want to rock the boat with this girl, because she's obviously wealthy and probably pretty domineering.