Asking how society would react is nearly always too broad.
There are many aspects to society and the view of society towards certain topics changes basically yearly. As an example women couldn't vote until december 2015 in saudi arabia. That's not a long time and for many people from western countries it's one of the most normal things today that women could vote, even if Liechtenstein allowed women to vote for the first time in 1984. Our point of view changes constantly.
The next thing is that there are too many aspects to society to discuss them in a post on StackExchange. There is a character limit of 30,000 characters on the site and people are writing a lot of books about topics that discuss how something would change society from their point of view.
Connection to the question from the OP
This is exactly what you are trying to do. You explicitly state that you want to write a short story about this topic and ask about the content of this short story. While there is no official definition for the term short story regarding word and character counts this statement already indicates that you plan on writing more than a concise answer that fits on the StackExchange site. A general rule of thumb when thinking whether a question might be "too broad" for the site is "Could you write a complete book to answer this question?". You can when asking about the changes to society by introducing a change that affects our current definition of society.
Discussion about the other questions mentioned
You are right in that broad questions are asked quite regularly on the site. WorldBuilding has the problem that it's not always as easy to draw the line when it comes to things like "opinion-based" and "too broad". In the answer I linked above I write a bit about why I think it's not easy to draw the line and that it's more some kind of blurry region than a line. This applies to "too broad" just as it applies to "opinion-based".
The first question you linked about the lie detector was posted only 2 hours ago. That's often not enough to close a question so it might still get closed. In fact it was closed roughly 5 hours after being asked. Especially considering that the weekend just started and that there is less activity on weekends. I already flagged that question as "too broad". You are absolutely right, but it's not really a good example. I am pretty confident that the question will be closed in it's current form as there are no constraints and two big topics are named.
The next one was about moving a planet. That's a clear scientific goal and it aims at maths and physics. Those questions are easier on-topic as there are less opinions involved. This is why it's easier to differentiate on-topic and off-topic questions on sites like Maths.SE, Physics.SE and StackOverflow. That question is on-topic.
The third one falls into a similar category as the first one. It was posted today and has a pretty broad scope without a lot of constraints. 19 hours is a bit much, even for the start of the weekend. So here another point applies: sometimes things slip through. You can't draw a perfect line and say that something is on-topic or off-topic and so the process sometimes takes a longer time and sometimes a question is off-topic but there are enough people online that have a more relaxed view and so the question is left open. Please help by identifying these questions and bringing attention to them by coming to the chat or posting on Meta.
You need specific aspects of society
Your quote mentions specific aspects of societies and cultures. You are asking about society in general without making any effort to say whether you mean "current day America", "current day Europe", "current day Asia", "near-future dystopian post-apocalyptic Africa", "people-accepted-genetic-engineering-but-otherwise-it-is-the-same-as-Europe" or any other possible definition of "society" for a work of fiction. You also don't mention which aspects of society you are interested in. Furthermore it is a very sensitive topic. You make the best effort to mitigate this problem that I have seen on this site so far and I congratulate you on being especially clear about this. Sadly some people might not be as willing to accept such a premise so easily and as we are all humans our political views may from time to time cloud our view on things. Just like not having had a coffee today might lead to someone clicking "close" more often one day than any other. There are a lot of possibilities but normally the Close/Reopen process takes pretty good care of this.
Currently I think your question is too broad, just like the forst one you linked and probably the last one, too. The one in between is on-topic. Thanks for bringing this discussion to Meta. These discussions alwasy come up and it's important to have them - we will probably never get rid of them. That's the nature of WorldBuilding under the rules of the SE network.
Now on to trying to help you, though I can't vote to reopen and the choice is in other peoples hands
- Try not to use phrases similar to "How would this change influence society?" <- those are basically trigger words for a lot of people
- as your text is pretty long some people might not have read it completely and looked at the title, the first paragraph and the last one as those are the most important ones
- try changing the title to something more focused, such as for example "What are the most important factors that would protect the idea that genetic differences leading to newborn gender disparity should not be modified?"
- try to rephrase the part about "changing current society" to something like "encouraging people to view [...] as normal" so that it's more about actions to be taken to change the view on the topic in the eyes of the public
There is no guarantee that these changes would get your question reopened or that your question could be answered here in the form you wish. It's a very difficult topic for a site on the SE network as it is aimed at starting a broad discussions that would get you the input of the personal view of the answerers to a very broad topic.