Given that this technology is politics-independent in that it can be used to cure Fibromyalgia as easily as it can homosexuality, what changes in our current society would be required to permit social mores to exist that would protect the idea that genetic differences leading to newborn gender disparity should not be modified?
These ideas already exist.
This comes up in a number of different ways. First, if the government determines if they will pay for a procedure or not, and if insurance doesn't cover it. Second, homosexuals, while they can have treatments to have children, don't have children through the natural course of their relationships as breeders do. More homosexuals, not less, may result in the government's effort to stem population. (The fourth child must be homosexual, for example).
Today, the bar for insurance paying for sex reassignment is pretty dang high, as are the hormone treatments afterwards.
Communities Sticking together
Being gay isn't life-threatening, neither does it cause constant pain EXCEPT in a society where it isn't accepted--what this means is that it cannot be absent of politics. Politics and religion would for sure play a part if the effort was to eradicate this population.
It's even more fraught than the deaf community's fight to keep their way of life. They like their community, they don't think that there's anything wrong with not being able to hear, and so, some choose not to cure their children with current science.
God created man in his own image. Does God make mistakes? The Vatican, Presbyterians and other Christian offshoots have begun to tackle this issue. Questions, such as "is the human genome sacred?" and "is humanity wise enough to mess with a process God has wrought?" are among those currently being asked. It's not beyond the pale that at least one or two major religious groups will say no to this, or have very specific rules against tinkering beyond a certain point. Other orders will go in the opposite direction, embracing this ability as a gift from God.
Choice of Identity
If an adult can have the surgery later, some parents will want to wait for their children to chose. As some parents decide not to circumcise--either because of family tradition or because they have researched and decided not to. In the case of gay, they might know gay people in their family and accept it, as one sort of identity, or they chose to allow things to play out.
Choosing traits might mean that everyone is a little too...similar. If blue eyes are popular, and connected to other genetics which seem insignificant at the time--it may open the door to disease/viruses being able to attack a significantly larger population. Monoculture leads to disease--or being vulnerable to a particular thing. A diverse population is a better bet. If certain traits become popular and EVERYONE decides to get them, that's a set-up for disaster. If I were the government or a medical body, I would not allow, in a given year, more than a certain number of children genetically modified to have particular traits.
Gender and Sexuality is complex
Gender identity is really very complicated. There isn't any one thing that determines it. You are starting with the "IF this were possible" premise, but of course everything from hormones in the womb, to epigenetics, to brain chemistry, and actual xy xxy yy genes determine this.
IF this were possible, the number of changes that would need to be made in a short span of time for a newborn, might well completely change the child in ways that aren't as foreseeable as you might think. In other words there will be people who will believe, rightly or not, that this sort of fiddling causes autism or social problems later in life. (Of course if EVERY mental and social issue can be corrected via this... that's different.)
People may believe that something of value is lost
How many stories have you heard of geniuses who couldn't be social? Or of people whose differences lead to greater things? How many stories exist right now of people who, when they couldn't be physical, turned their mind to other things? How many people became great artists because they were different in the way they thought and looked at the world? And how can we know that "fixing" the gay and other things doesn't lose us benefits as a society and as individuals?
Was Einstein flawed as a baby? Would the genetic fix also lose us a Mozart? How about Stephen Hawking?
Genetics and experience are like a pile of paperclips. I can easily see groups making this argument. (It's somewhat flawed, but it is an argument that would be made).