Many unbelievers are very intelligent and thoughtful people. A lot of them are downright nice, and even gracious. Sometimes they put professing Christians to real shame.
My experience with them is that they are very liberal in their thinking. They live the way they want to; they have pretty much cast off (and often very consciously) all vestiges of organized religion; and they seek to spend the days they have on earth having as much fun as they possibly can.
The question before us is this: can these people be reached with the gospel; and, if so, how? My answer: Yes, they can indeed be reached; but the way to do so is not according to the standard approaches being employed today (by many churches).
Intelligent unbelievers are wary of gimmicks, and of believers' efforts to mimic the world. They know we cannot do as well as Madison Avenue does, in marketing our religious wares; and they snicker at our paltry efforts to act like Hollywood, often viewing these antics as little more than jokes.
Unbelievers need to behold serious and intelligent believers, living life in church, intentionally and consistently. The best way to reach intelligent unbelievers is to be faithful churchmen. The churches we belong to ought to appear to be different from anything unbelievers see in the world all the time. In other words, "contemporary" is not the way to go. This may snare some mindless unbelievers; but typically, it will not entice thoughtful ones.
Let our churches employ the old Puritan ways: filling the pulpits with men truly called to preach the gospel, who are well-trained, and fluent in the things of religion and the world. Let us sing psalms and hymns; and let us pray earnestly. Also, let us employ the Lord's Supper and Baptism, as signs that distinguish God's people from those who are not His.
There is no guarantee that intelligent unbelievers will respond positively to our gospel message, even in the context of a serious church worship on the Lord's Days--but it is their best shot at glory.