I'm not going to respond to every dumb thing that has been posted on this thread.
I'll just say this: I've been involved with more than one custody case with a child who is this young (or younger) with gender identity issues. I've seen it where both parents support the kid, and I've seen it where one parent is adamant that in their care, the child only wants to express as the birth gender and the parents are at each other's throats about it.
What you can't loose sight of is that this is literally a life-or-death issue for the child in many cases. And I don't know a single parent who wants to cause their child's death. So you can make all the glib jokes you want, but keep that in mind.
It's absolutely a real thing, gender dysphoria in adolescents is a recognized diagnoses in the DSM-IV. You may also hear about a child being "gender fluid" or "gender diverse," but those are really different sides of the same coin. There is some dispute about whether gender dysphoria should be a clinical diagnoses - but it's not because it's not real, it's because some experts don't like it being treated as a mental health issue, and having that stigma. But the fact is that a child's external sex organs absolutely can be mismatched with the child's internal psychology is almost universally accepted - both in humans and other mammals. It's not even really controversial in the medical community (their are splinter groups who claim it is - but it's not).
A six year old absolutely understands gender and his or her personal identity, in fact children start expressing their gender identity under 6. Think back to your own kids or yourself if you can - you/they probably knew before kindergarten if they were a boy or a girl. Gender, however, does not mean sexuality. A six year old does not understand sexuality (if they do, that is a sign of sexual abuse) - and this shouldn't be confused with gay/straight/bi type of thing. This is about a child expressing their gender identity, not a sexual preference. You have to unlink the two in your mind, because they don't have the link until closer to/after puberty. I've had an expert say in a trial on this type of issue that an easy way to remember is "Gender is who a person goes to bed AS, Sexuality is who a person goes to bed WITH." Six year olds aren't going to bed with anyone.
No one is going to start a 6 year old on any sort of hormone therapy, or do any sort of surgery. That is years away in the best/worst case scenario depending on how you look at it. And it would take a team of doctors to sign off on it, after years of going through a medical evaluation process. At a minimum, a pediatrician, a psychiatrist, and an endocrinologist. And probably some sort of therapist as well. It's not something a parent can just go to a doctor and have done. That is asinine that anyone thinks that would happen just because a parent "wanted it."
The kid needs to be in therapy to see if this is a phase they grow out of, or if it is something that is permanent. And the kid needs to be the one to lead, not the parents. And the kid needs to be supported, not judged, or not forced to please a parent. The real risk here is the child committing self harm or suicide if they are not supported by their family. A child with gender identity issues who is not supported by his or her family is 8 times more likely to attempt suicide, six times more likely to experience major depression, and four times more likely to use illegal drugs than a child whose gender identity is supported by their family.
Make all the jokes you want - but I come down on the side of having a live child, whatever gender they want to be, rather than on the side forcing a child to live the gender you think they should and causing the child to kill themselves.
But that's just me.