To look at it from the other side - the parents haven't given their child much privacy here. That child is going to face the cruelty of other children (and people in general) due to the fact the parents have blogged publicly on their child, and are happy to show the media the child's face and talk about the child's preferences, etc. It says in this article that Woods has said such parents are making their child "a target" [for harassment]. The internet never forgets as we know. Those words and images are going to be there even when the child has grown up and may or may not feel the same way as the parents claim he does now.
While it's none of Wood's (or anyone else's) business what somebody does with their child's upbringing, he has a point. If I were a parent, I would never sell my story to the press and publish my kid's name and face for the world to see. My child isn't a toy to be paraded around but a real person whose opinions and ideas may well change with time - as a parent it would be my role to keep them out of harm's way until they can look after themselves and choose if they want to be in the limelight. If my parents had done that with me I would be angry with them at this point because I value anonymity. I would not want the entire world to have known how I felt at the age of ten.
I've noticed a few articles floating around lately of parents who may or may not be using their trans children for the purposes of attention and possibly money for selling their story to the press. Some of them seem more blatant and some less so. But the overt ones do not have my support. If you're an adult and want to publish your story - fine. I am not in favor of plastering your child's private life all over the internet, though.