We could solve that now, without Gene's replicators. It isn't technology that keeps us from doing it. It is lack of love.
We have the technical means to feed all the hungry on this planet, but we don't have the technology. You really think it's possible to feed the hungry on this planet simply because the food exists? Do you have a plan that allows for the hungry to be given the food of the more fortunate? Because there are a lot of people trying to do it and there are still hungry people. In fact there are millions more people in our contemporary day that have solving world hunger on their "to do" lists and there are still hungry starving and dying people. Why?
I'll tell you why. It's because we don't have the technology to do it because if we did there would be no world hunger issue. We are close to having the technology but there are a variety of other factors to consider. Such as economics, government, prejudice etc. Remember all this technology we have now is exeedly new. Our species has not had a whole lot of time to figure out issues like supplying the world with food because for the majority of our existence we never had to worry about such things. We are still in the past from the brain's evolutionary perspective and that means a survival based framework. I won't argue that that framework is fading away and rightly so.
Not only is the "lack of love" answer insulting to the human race it's also a useless answer because we can't fix "lack of love." As you Chritian's so aptly agree with when you say "only Christ can save us." Your explanation encourages giving up.
Technology is the answer. But preaching Jesus message of love is also the answer because once technology catches up we can hit the ground running driven by the power of the love we have already become accustomed to.
-Sab