Case insensitive sorting with Firebase orderByChild

You don't. Kind of.

If you have data you want to sort by but there also needs to be a user representation of that data, keep two versions

posts
  post_id_0
    display_version: William
    sort_version: william
  post_id_1
    display_version: Henry
    sort_version: henry

Of course you could read in all of the data from Firebase and use .toLower or whatever your platform call is and then sort in code.