I believe that "it" in the case of "it's me" or "it's John" is an expletive. Like Coline Fine commented above, it is a syntactic placeholder, because in English we can't just say "is me/I am" or "is John/John is" (which is fine in other languages, e.g. Spanish). So, dictionary.com is being extremely misleading in the "it's John" example, or even outright wrong, depending on your theoretical point of view.
It's the same expletive-it that shows up when we say things like "it rains a lot here". What rains? The word "it" is here simply because we can't have a verb without some sort of a subject in English; it doesn't refer to any explicit thing.
So, I would say that we don't use "it" to refer to (non-infant) humans, and "it's John" is not a counterexample.
A hundred years ago, in English, the standard gender-neutral pronoun was clearly "he", but in recent years we started finding it inherently sexist. As a result, we are in a wishy-washy period in English where there is a need for a gender-neutral pronoun, but people aren't quite agreed on what it is. In my observation, "they/them/their" is emerging as the clear frontrunner -- certainly this is true in spoken and informal speech.
"I just got a call from someone at the doctor's office."
"Well, what did they say?"