Didn't read the OPs later comment about abuse. Apologies.
You presumably are an adult, who has internet access. Did you not know that abuse is a thing that happens before the OP mentioned it, or what?
It always amuses me when people say "Oh, no. Far too young for a sleepover. Why not ask if the friend can have a sleepover at yours instead
I assume those people are actually aware just why mothers are worried. It is a matter of trust, and everyone trusts themselves, so if the other mother is willing to trust a relative stranger, problem solved. The "child is too young" is more of an excuse to not have to talk about male violence. Because no one is allowed to mention male violence.
Fearing male violence is "irrational", apparently.
So women resort to pseudoreasons.
I'd certainly not be worried about a child only eating junk food for one day, or even about not getting any sleep if the next day isn't a workday or a schoolday.
You can never be perfectly safe, but I'd at least want to have seen all family members, and have had opportunity to observe how they act around children, before trusting them.
With mobile phones, there's an additional safety net, but it depends on how vulnerable to peer pressure the child is. Some children may not want to call their parents for fear of what the other children might think. (And unlike some other people, I do not expect children to be able to predict exactly what an adult who made them uncomfortable will do next, and to weigh that risk against the risk of seeming odd to their peers)