For me, it depends on the age and setting.
With both children, I exclusively breastfed and pumped. By the time we moved to solids, their providers were very clear that I had specific ideas about feeding children. Ex: I would rather pick them up early and nurse them as opposed to giving them a bottle at 4:45.
I have a strong history of food allergies, so when we moved to solids I was very specific about what foods were OK, and what were not. Both DS and DD had dairy sensitivities through late infancy, so daycare knew not to give any foods without permission. It just evolved from there.
Diet and compliance is one of my 'litmus' tests for daycare. If I cannot trust them to respect my wishes, then I don't want them caring for my child.
I think it is more a concern as the kids get older, and there are more 'pizza days' or birthday celebrations. Then you need to go with your gut and your knowledge of how diet affects your child. DD is about 80% primal now at age 7, started at 5. We limit the pizza, but are OK with cupcakes at birthday celebrations, etc. It does not seem to have a negative reaction for her.
DS is more gluten sensitive, so we will need to be more aware of the frequency or amount. When there has been a birthday at his current daycare I have provided a 'safe' snack for him to have along with the other kids. I am not against a GF cupcake now and then.
My goal is not for kids to be 100% primal no matter what. That dogma just will not work for my day to day life. If I can control their breakfast, lunch, dinner every day, I am not going to lose sleep over an odd snack or pizza lunch.