I don't know how such a situation might have arisen, but evolution will solve the problem... with perhaps a little help.
In this species, males and females are rarely if ever attracted to other individuals.
This may seem to mean that people aren't interested in sex, and it does mean that for most people that is true. However, it also means that some people are interested in sex.
As long as some people are interested in sex, all is not lost. All the government need do is identify these sex-liking individuals and bring them together and provide them with incentives to indulge in sex and to reproduce. With enough incentive, the government reproduction program may well recruit those for whom sex is merely 'a bit yucky' as well as those who like sex, and that's fine... anything is an improvement over total disgust.
As these people reproduce, they will tend to produce offspring who are not totally repulsed by sex, and by breeding these new sex-positive people with one-another, over generations, the people will come to like sex and won't need to be subsidized to reproduce.
It doesn't even matter what the cause of the negativity toward sex may be... the people can evolve a counter to it.
There is practically no easier condition to evolve out of a population: those with the undesirable condition literally won't want to reproduce naturally anyway.
Additionally, if there are females who find sex repulsive, but aren't averse to bearing children, they could be implanted with the in-vitro offspring of sex-positive individuals to boost the birth rate.