Parents should not support their children because they are confused.
Children lack the experience and logical thinking to properly decide on matters as such. Most children have probably thought about how nice it would be to be of the other gender because the grass is always greener on the other side with their childish thinking. They are unable to weigh the pros and cons and logically interpret many things (especially their own feelings). And by children here we refer to persons below the age of 12. I support letting your boy play with dolls and your girl play with cars and not imposing gender stereotypes on them but that's as far as I'd go. They do not fundamentally UNDERSTAND the implications of being transgender and what that is even all about so there's no way a responsible parent should support them on that.
I prefer trial and error of my job if it means my freedom to choose.
A right to choose is what makes the world go round. We are given free will as much as possible and I believe a career is something one should be greatly interested in so as to achieve their own happiness and possibly contribute back to society/ aiding humankind's advance. If even such things are predetermined I do believe most people will not be productive in their jobs and also there will be many instances of bias because somethings simply cannot be judged.
Abortion is not murder. The child has not been born. Pregnancy can be a decision period for parents to decide if they want to bring this child to this world? If they are able to feed and clothe him/her? It's all up to them (do believe a woman has more say however as she is the one carrying the child, cannot force her to abort/carry against her will). The 'child' has no consciousness. Is crushing a seed chopping down a tree?