I did have a little girl with a nut allergy in my care for over 2 years and I carried an epipen and read every label and was super cautious all the time. But it wasn't a problem for me, just a new challenge.
I have a lactose intolerant boy in my care and the parents are responsible to bring his cheese and milk all the time. I would accept a child with a gluten allergy or a vegan diet into care but I would ask the parents to send all the food. I wouldn't change my entire menu for them.
It is a problem when one child has something different from all the others but if you teach them the reason they will understand. I always tell my children that my lactose intolerant boy has to eat different foods because our food might make him sick and they accept that without any further questions. Actually, they have told other people about it when we are out, ha! And when I had the nut allergy girl in care the other children were helping to look around at the park for nutshells the squirrels had dropped. They enjoyed helping to take care of her.
It all depends on your point of view and routines and of course, your relationship with the parents and how well you can work things out. My nut allergy girl had the most amazing parents who gave me all the tips their doctor gave them. It can be done, but as the other ladies mentioned, you have to weight the liability fear against your honest abilities to deal with the situation.