Trusting anyone with your child, whether they have allergies or not can be difficult. For parents who have children with food allergies, this becomes even more terrifying!
I asked my mom what her experience was when I was little. She told me for the first few years they used my aunt and my grandparents as babysitters. My mom told me that the first babysitter that she left me with, ended up giving me a piece of candy one time that she had with her. Luckily I wasn't allergic, but she didn't check with my mom or anything! My mom said that after that they were even more careful. My parents were lucky because my grandparents and aunt weren't too far away.
Once I started going to nursery school, I used to go over classmates' houses for play dates. My parents always sent me with my own snack and the same snack for my friend. My parents made me responsible at a very early age, so although they could get nervous, they usually felt okay sending me places (remember, I was the only one in any of my schools that had any food allergies, so it was extremely rare). My parents were great about educating everyone who was around me about what they needed to do! My parents were also able to become close with my best friends' parents, so they were all like second families to me. I always felt very safe going to any of their houses.
As I got older we had more babysitters. In my second year of nursery school, my teacher would sometimes babysit me, and she stayed with me when my parents were in Europe for a few weeks.
It really comes down to educating. People are now becoming more and more aware of food allergies. If you can educate them and feel like they "get it," then that is great! It is also very hepful having close family and friends who you trust to care for your children!