For most of history, having children was essential. Agrarian peoples needed hands to work the fields, monarchs needed heirs to take their throne, craftsmen needed people to pass on their trade, etc.
Obviously, none of these needs require having children, but it is very convenient for a number of reasons. Rather than having to bring someone into your work and having to pay them, a farmer doesn't have to pay the children. In the case of those in political power, a child can be much more easily influenced and trusted than an outsider.
All of this was furthered by distrust of people who are not friends or kin.
So in past centuries, outright refusing to have children in many cases was not a very good plan.
I focus on the aspect of having children here, rather than intimacy or love, because those ideas were not really important to many people prior to the last few centuries. Obviously, people did find love with each other, they weren't heartless or anything, but most people were marrying for matters of necessity.
The enjoyment of sexual relations also were secondary in many cases to having children, and in many cultures, certain things weren't even recognized regarding sex (such as female orgasms).
So for a whole society to so aggressively turn against any kind of relationship... that's a bit questionable. I can see strong taboos against romantic love in a certain culture, but such a hard stance against something so useful as having children would be rather odd.
Even today, where some may characterize this as happening, where a number of young people in the developed world are deciding to not have children, this is hardly out of an outright refusal to do so a lot of the time. Many prioritize work. Others would like to have children, but can't find the right person, others feel anxious about raising children in current economic conditions or with threats like climate change hanging over their heads.
All a number of reasons why people are choosing not to have children - and then you have people who get married and have children just because it's what they were raised to believe they should do, and have no really interest in it.
Then there are people who are similar, not knowing any other direction, but finding a desire to be married with children. Further, you have people who are very strong in support of having children from religious beliefs.
All in one world - and even, as I said, the developed world, a large cross section of different people. Only at the far fringes do you have people who are staunch anti-natalists or are quiverfulls trying to have as many children as possible.
In real life, there is no group who is a hive mind. There are certain inclinations, but everyone will be different, and even if they have the same views, they will have different reasons for believing in them. This is my long winded way of saying that you should perhaps acknowledge that, unless you are going for a quite alien group of people, there will be diverse groups within it.
You will have people who find intimacy and relationships disgusting, but need offspring for aforementioned roles, as workers, as people to train in your trade. You will have people that do find love - maybe not romantic, sexual love, but a sense of belonging with others.
Civilization is built off of people working together. If people hate being around each other, I have a very hard time understanding how civilization would exist in the first place.
So, to your final question, what can the government do about this?
The frustrating answer - not much. In real life, many governments, notably Japan and Germany as two examples, are watching their populations age with no replacement occuring. They are trying things like monetary incentive to get people to have children, but this doesn't seem to have much results. Japan is trying to replace a lot of jobs in the country with robots, and that is a temporary solution.
Other countries with these problems, to sustain their population, are turning to immigration which has a lot of conflict surrounding it. This is one reason why the US doesn't need to worry about declining birth rates for a while, as the growing immigration from Latin America is keeping things stable.
But eventually, something has to give. Immigrants will become the majority, or the population will decrease significantly, causing the nation's power to wane.
But as mentioned above, there are so many different types of people - and there will always be people who want to have children for one reason or another. So in the refusal of some in your world to have children, those who do will be the ones who steer the ship. Their view of the world will be what shapes broader society, as they raise children with their beliefs.
I'd imagine your society would reach a point where people decide to have children merely out of survival reasons. The country is collapsing and there's a massive labor shortage, and having children, especially very bright, skilled children, may be seen as a badge of honor - others might be awed that you suffered the horror of having a relationship so that you could have a child.
I doubt governments would be able to have much influence with this, other than fueling a fire that was already going.
This of course assumes that your country is somewhat democratic. If you're a totalitarian regime, you just tell people that they can't have food unless they have kids. This of course would lead to many awful, awful acts, people having children and then abandoning them so they can have certain benefits without the responsibility.
So... yeah. I apologize for such a long response. Population and its changes can get really complicated, especially in such an odd situation as the one you described. I recommend studying population growth and decline, looking at the reasons why changes happen, etc. Japan and Germany are good ones to look at, China is a peculiar look into what happens when harsh population control is enforced and all the problems it can cause a country.
I hope that my scatter brained thoughts have provided some insight, or at least direction for where to look for additional information.