Um I'm a CM and have called parents before. Cast members are allowed their personal cells now (have been for at least 2 year) we just aren't allowed to use them on stage. I have handed my phone to a lost child and have even called the parent myself. When you have a crying child next to you most guests realize what is going on.
Also I have used my personal cell to call 9-1-1 because the company phone was broken which I was specifically direct I am allowed to use and they even have a word for word what the first sentence should be if and when you have to call from your personal cell.
Now if you write your information on the child they need to know to present that information to the CM. I am not allowed to take off shoes, look on clothing tags, take buttons off and look on the back etc. Now if your child comes up and says I'm lost here mommy's cell is on the back of my magic band then I can ask them to take it off and hand it to me. At that point I radio my manager let them know I'm with a lost child and I have the parents information so will try calling them. There are hundreds of hidden phones all over property that I can use if they don't want me taking my personal cell out.
Thank you for this information!