I fully support trans people and their choices to transition, as long as they're very sure that they're being true to themselves. In my opinion, if you were born one gender but truly feel like you like you identify with the opposite gender more, you need to do whatever is necessary to feel comfortable with yourself and how you interact with the world.
With that being said there are many people who regret their decision to transition and end up living in misery, hurting themselves and in some extreme cases taking their own lives. I completely support sexual freedom and freedom to do what you please with who you please, so long as everyone involved is a consenting adult. But having surgery to change your physical makeup is a serious, irreversible decision and as much as I think that trans people should have the right to transition, I do not believe that right stands for children.
If you live in a home where your parents do not support you, my advice would be to get out as soon as you can, especially if you're being neglected or abused because of who you are.
If my child told me they were gay or transgender I would not be bothered by it at all. It would be about as important to me as their favorite flavor of ice cream in the sense that I could care less who they love as long as whoever they date or marry treats them well.
But transition surgery is very serious and is something that should be thought about for quite some time before any kind of decision is made.
Long story short, no, a child should not be able to get that kind of surgery without a parent's consent.
“Love is the only bow on Life’s dark cloud. It is the morning and the evening star. It shines upon the babe, and sheds its radiance on the quiet tomb. It is the mother of art, inspirer of poet, patriot and philosopher.
It is the air and light of every heart – builder of every home, kindler of every fire on every hearth. It was the first to dream of immortality. It fills the world with melody – for music is the voice of love.
Love is the magician, the enchanter, that changes worthless things to Joy, and makes royal kings and queens of common clay. It is the perfume of that wondrous flower, the heart, and without that sacred passion, that divine swoon, we are less than beasts; but with it, earth is heaven, and we are gods.” - Robert. G. Ingersoll
It is the air and light of every heart – builder of every home, kindler of every fire on every hearth. It was the first to dream of immortality. It fills the world with melody – for music is the voice of love.
Love is the magician, the enchanter, that changes worthless things to Joy, and makes royal kings and queens of common clay. It is the perfume of that wondrous flower, the heart, and without that sacred passion, that divine swoon, we are less than beasts; but with it, earth is heaven, and we are gods.” - Robert. G. Ingersoll
