How do you respond to non-Christians who say they have an open mind?
What you say depends on what you know about their background, their intellectual and emotional orientation, their parents and how they were brought up, and their experience with church and the Bible, etc. There are so many variables. But here are a few ideas:
1) People need to be brought face to face with how utterly unique they are in the universe of God's creations and in his animal kingdom. Help them see that they have capacities for love, hate, guilt, and grief. Help them see that these are not the result of mere chemical reactions.
No one wants to say that their love for their child is merely chemical, or that their reverence for a good and wise person is just a reflex of nerve endings, do they? Most people say, No! Then you can help them deal with the fact that personhood is a tremendous mystery and in an entirely different category than what they are so ready to talk about in regards to evolution. They don't want to treat themselves that way, by and large.
Don't you stand in awe of your own personhood? I would tell them about how I sometimes sit around a staff meeting at church or a lunch with my family and look at other people and say, This is incredible. Just look at these human beings and what their thinking and feeling and planning! It is amazing that something exists in the world that is so different from lizards, frogs, horses, and monkeys. This is so different! Where did this come from?
Then I would tell them that they should really want to be open to the fact that there is a personal God who created this reality in his own image; and therein lies the explanation for your unique personhood. If there was only an everlasting gas out there, some big bang thing that has no explanantion, and that everything was just matter, then your existence and family structure and business plans would be absolutely inexplicable.
2) Another approach would be to consider the universe--with its order and beauty--and approach the concept of intelligent design, which is so alive and well in the world today. So many people are writing good things to help us understand that the complexity of the atom (and the eyeball, and the universe, etc.) is such that it can't be explained without intelligent design. Then you start talking about God.
3) A third possibility, which I think is the most fruitful and would be most leaned on, is to talk about guilt, sin, God, death, and the possibility of forgiveness and eternal life. Then you present the gospel--the sheer raw and glorious facts that 1) God is holy, 2) I'm a sinner, 3) Christ died so that he could take the place of sinners who trust in him, and 4) are you willing to trust this Jesus? A lot of skeptics are prepared by the Holy Spirit for an authoritative and true remedy of their sin problem. And the Holy Spirit will enable the gospel, shared simply, to click deeply in their hearts, so that there is an evidence in their own soul that this is true.