Your OP kind of frames the debate by using some loaded language that isn't really present in the examples. You claim that these parents are pushing their children, however in both examples you provided, it appears that the children are the ones who are being allowed to lead and express their own identities in the way they see fit. In my opinion, the only way to see such a thing as child abuse is if your own biases lead you to believe that Transgender identity is wrong in some way.

Where was anyone pushing a child to question their gender? What I read sounded like just affirming what the child said themselves rather than anyone pushing a child to do one thing or another.

The psychiatric community appears to think so. I tend to defer to the experts where possible. I haven't spent years studying child psychology so I assume they know more about it than I do. Hopefully if a psychiatrist had a question on bioinorganic chemistry they would afford me the same respect. 

Agree with op. That first link is just crazy. At 3 years old kids are just starting to talk they have no idea what they are saying.

I say parents should not encourage any of this. Once they become teens then take what they are saying into consideration. Maybe seek guidance. But when they are as young as 3 thats just the parent pushing that belive unto the kids.

Depends on the situation. 3 is pushing it but in some kids stuff like this crops up pretty early. Legitimate hormone treatments and the transitioning process probably shouldn't start before around 15 or 16 but it's not absurd for someone younger than that to at least partially understand what's going on in their head.

First of all, transgender identity is not a sexual preference. I'm not sure if that is what you were implying here, but that point should be made entirely clear.

Beyond that, what is the harm in allowing a child to express themselves as they see fit? In my opinion, a parenting style of forced conformity is often far more damaging to a child's development than allowing them to discover their own identity without undue pressures. Again, the only way in which I can understand someone coming to the conclusion that this is child abuse is if your own biases lead you to believe that Transgender identity is wrong in some way (ex. morally).

Puberty doesn't play a role in this discussion because a person's identity has nothing to do with sexuality. Using the word "encourage" is pretty shitty in this case, as it makes it sound like the parents are pushing the kids to make a decision. It's not something you should encourage, but it's something the child should know about and something that should be supported in case the child feels that way.

Transgender identity at a young age can be fake yes,in some cases it is pushed onto autistic children that are already socially confused and could very well think it is because they are supposed to be the other gender and you should care about this possibility,it is important for both the transgender community and the children involved.

Im not saying there arent real transgender indentifying kids but it is open for abuse and each situation needs to be very carefully looked at.

When I saw "wrong" I mean morally, ethically or religiously or something of the sort. I will edit my post to make that more clear.

A 3 year old has no clue what a boy or girl even is. So its one thing to just play along until the child gets older and understands, but even doing it that will just confuse the kid even more by the time he is able to understand whats happening. So if a kid has no idea whats happening and the adult is going along with it then yes that is encouraged behavior. 

At 3 years old, kids want to be firetrucks and mermaids and princesses. They know same about sexuality so the adult going with it is just harmful to the kid.