I am all for people being themselves without being subject to judgment or ridicule, but I also question at what age it should be acceptable to allow young children to make such choices for themselves.  Tough call and I think I can see all sides.

1.  Allowing a kid to identify as a different gender at one point in their lives does not force them to maintain that gender.  Kids change their minds about lots of thengs for which they adamantly feel. While I don't think gender is one of those, if it was, then allowing flexibility wouldn't cause less flexibility.

2.  Actually you have plenty of evidence in your own experiences that most kids do strongly identify as a gender at an early age regardless of what the parents do to be neutral.  We just don't notice this because in the vast majority of cases, they identify consistent with genetalia.  

3.  In the absence of evidence of harm, we should trust the judgments of the parents, who know their children far better than we do from our comfortable distance.  That is what any of us would want if it was our child who was not fitting in.