People are going to do what they're going to do, but in my opinion, the hyperawarness of binary gender beginning before a person is even born is part of what makes navigating the gender spectrum so challenging later. When your parents are celebrating you're a girl or a boy before they even meet you? Focusing so much on gender rather than on having healthy, well-adjusted kids? Why do we see videos of parents say "oh thank goodness!" at gender reveal parties? Or cakes that split the genders into activity groups before the kid can even tell you that they like pink AND soccer? You could even say that children are not so much born with gender, gender is simply ingrained in children before they are even aware of what it is.
If a child does not choose to be something other than their biological gender, then nothing anyone does is going to change what they are or are not. Babies are a happy occasion and parents are always thrilled to find out they are pregnant and then excited to find out whether its a boy or a girl. And whether they like pink and soccer in the future or blue and baseball or green and cats has NOTHING to do with a cake the parents have made before they were even born nor does it have anything to do with what gender the child is or is not.
Why do we see parents saying "thank goodness"? Because when you have 6 boys and you want a girl, that is your reaction. Does that mean the parents won't love her if she comes to them one day and says "I am not a girl" Of course not or it shouldn't.
Perhaps gender shouldn't be pushed on a child but neither should the confusion of thinking about their gender when they aren't questioning it or confused about it or thinking they were born the wrong gender or whatever. For the vast majority of kids, its not something they should really even think about.
As someone who worked for 16 years with children ages 0-5, nothing has to be ingrained into a child. They naturally gravitate toward much of what we view as "traditional" boy or girl tastes and likes--which is exactly why those things became thought of as traditionally for a boy or a girl. Put a group of boys in a room with several choices of items to play with and almost every one of them will go toward blocks, trucks, etc. The girls will go toward the dress up, kitchen, dolls, pretend play things. ALL of them like art and science. Take a group outside, most of the boys will play rougher than the girls. You can argue gender till you turn blue but 16 years and hundreds of kids will tell you otherwise. No one is ingraining anything in them, its just their natural way of being. That does NOT mean girls can't be rough and tough or that boys can't enjoy pretend play and quiet play. They all will do all of it throughout a day, but MOST of the time, they will naturally go toward the things that are seen as "traditionally" male or female.
What needs to stop is the adult thoughts and needs being pushed on children. Let them be children. They will get into enough confusion with puberty starts. Some parents are now trying so hard to meet all the new thoughts on these things that they are confusing these poor kids more.
I know a young lady that is so hell bent on making sure her son knows that if he is gay or trans or whatever, she will still love him and accept him that she is bordering on making him think he has to be one of those for her to love and accept him. When all he needs to know is that she loves him unconditionally. That's all any child needs--unconditional love.
Children and parents do not need the added confusion of being "oh so careful" about "pushing" a gender. That is rubbish.