I firmly believe 100% in the sovereignty of God in the work of salvation in a persons life, but I also believe 100% in our responsibility to share salvation. I think the confusion comes when we misunderstand the parable of the sower. We are told to cast the seed, we are not told to make the DNA of the seed to replicate through mitosis, nor are we commanded to develop chloroplasts in the leaves of the seed as it grows and produces chlorophyll. Neither are we to be the light that causes this chlorophyll to generate the food necessary for the plant to live. We do two things, plant seeds and water seeds. For us, the trust must be absolute that God is going to do all the work. Being born again is the analogy Jesus used to explain the new life, when my child was born I marveled at her new life, but I was also keenly aware of how little I had to do with how she became a human being.
I think often times today, people turn the parable of the sower upside down, and inside out. Instead of casting a seed that we should inherently trust God to bring to life, we cast fruit plucked from a tree that already grew, or we cut off a branch from a tree, and cast that into the ground. What I mean by this is that we offer people the "Fruit" or benefits of Christianity, and in so doing we have danced around the burning bush. We share the peripheral issues but have not cast the seed. For the Gospel is the power of GOD unto salvation. We must trust entirely and preach entirely the true and simple gospel.
I often pray that God would help me to know the gospel better and better all the time for it is so easy to think that I am sharing the gospel and casting a seed, when really I have cast something else altogether.
I can no more manipulate a seed into life than I can raise someone from the dead. This is a family business that the trinity has perfected, and I think they have a monopoly on it.
Your responsibility to any group of people is to cast the seed, you may reap thirty fold, fifty fold or maybe even a hundred fold, but I tell you for sure, if you are walking in the Spirit, and your preaching is a demonstration of the power of the Spirit, and the Spirit bears witness to your life in that you are not living in sin and quenching the Spirit in so doing, there is a good chance that you will be watering and casting seed when you share the gospel. Let God do the mitosis, and photosynthesis, turn carbon dioxide to oxygen. Only he brings people into the new birth through the power of the Spirit.
There was a book that J.I. Packer wrote called "Evangelism and the Sovereignty of God," that explained the balance between these two dynamics very well. I was not re-hashing what he wrote, but it is a book I would recommend on the topic. And you do not have to be reformed to understand and agree with his points at all. It is only a short 125 pager and he deals well with the balance.
I think you need to take each group or individual on a case by case, lead by the Spirit basis. Paul eventually washed his hands of the Jews, but he preached to them first always, Philip was whisked away from the Eunich, Paul was forbidden to preach in Asia. The Spirit leads, and I think we need to trust him with great faith to lead us in the sharing of the Gospel. Which starts every morning by taking advantage of His new mercies and walking in His Spirit.
Sorry for the long reply...kindof.