The notion (and that's all it is) that Christians have to establish long-term relationships with people in order to "earn the right" to share the gospel with them; the notion that we should let people see the gospel in us and thus making the verbal proclamation of the gospel unnecessary; the notion that "relating to people" (as it is most often taught and practiced by American Christians) is somehow a prerequisite for sharing the gospel has no Scriptural support. None. And any effort to draw such inferences from the text of Scripture is an eisegetical exercise that might make Christians feel better about their evangelistic disobedience, and might make pastors and their ministries more popular, but, in the end, will only prove to be a disservice to the Scriptures, Christians, and the countless number of lost souls who aren't reached by believers who practice such philosophies of ministry....
The Book of Acts and the letters of Paul are replete with examples where the disciples confronted people with the Law of God to bring them to the knowledge of their sin, before explaining forgiveness of sin through the penal, substituionary atonement of the Lord Jesus Christ.
No where in all of Scripture does God say that if we can just get the world to like us, they'll like Jesus. And that's just what today's "evangelical" churches so often think and how they behave. If they have "cool" music, an unoffensive message, have a big building with all the bells and whistles (including rock climbing, a cafe, "cool" "Christian" music blaring from speakers, casual dress, etc), then the world will be more "open" to hearing them. Such is the folly of an anti-biblical evangelistic view.
Appealing to the flesh (both spiritually speaking and physically speaking) to "get a foot in the door" is wrong. It's also manipulative and dishonest. It puts off the crushing blow of the Truth of the Lordship Gospel of Christ Jesus.
Joh 15:18 "If the world hates you, know that it has hated me before it hated you. 19 If you were of the world, the world would love you as its own; but because you are not of the world, but I chose you out of the world, therefore the world hates you.
1Jn 3:13 Do not be surprised, brothers, that the world hates you.