I am law enforcement and have have a kid actively run from me. (When the kid was reported lost, and the parents are looking for them.)

Guess who runs missing persons searches? Law Enforcement. (Often the Sheriff's Department).

In my case the child was also special needs, which was likely the barrier. (Stranger in a uniform with lots of gear on trying to talk to you). When I see parents with special needs children, if they are open to it, introduce myself to the kids and let them know I am there to help. (So if they later are in trouble, they met me in a safe environment initially).

I can't imagine how bad it'll be if people start training their kids to fear a badge.