The biblical basis for evangelical worship can be developed by a close examination of two key texts: 1 Corinthians 1425-26 and Acts 2. ... Earlier in verses 15-17 [in 1 Corinthians 14 - DHC], Paul insists that God be worshiped in such a away that it leads to edification. Now he tells us that worship must also be done in such a way that it leads to evangelism. ... Virtually every major commentary tells us that in verses 20-25, Paul is urging the Corinthian believers to stress prophecy over tongues for two reasons: (1) prophecy edifies believers, and (2) it convicts and converts nonbelievers. In other words, Paul instructs them to stress prophecy over tongues at least in part because it converts people. Why else would he give a detailed description of how a non-Christian comes to conviction in worship?
In Acts 2, we find further compelling evidence for evangelistic worship. When the Spirit falls on those in the upper room, we read that a crowd gathers... Again we find the church's worship attracting the interest of outsiders. This initial curiosity and interest eventually lead to conviction and conversion; in other words, it is evangelistic. [Tim Keller, Center Church: Doing Balanced, Gospel-Centered Ministry in Your City (Grand Rapids, MI: Zondervan, 2012), 302]
Keller promotes having church services which are evangelistic in nature. While certainly I would agree that churches ought to proclaim the Gospel every Lord's Day, that does not mean that anything which calls itself "evangelistic" would be accepted for Gospel proclamation during the service. When Reformed churches speak about Gospel proclamation, they normally mean the Gospel proclamation primarily in the sermon and also in the liturgical practice of the reading of the law, confession of sin and declaration of pardon. In other words, the Gospel proclamation is done in a certain manner congruent with the principles of God's Word, not in any way we think it should be done. Therefore, while I believe that the Gospel ought to be proclaimed every Lord's Day, that is far from the idea of having "evangelistic worship," whereby the task of evangelism determines how worship ought to be done in the church service.
In order to prop up the idea of "evangelistic worship," Keller raises two passages: 1 Corinthians 14:24-25 and Acts 2. Both passages according to Keller speak of how we ought to orientate our worship towards unbelievers. Keller promotes what can be called being "seeker-sensible," in the sense that the "praise of Christians" ought to be comprehensible. As we have seen in the discussion about contextualization, what "comprehensibility" means is that the worship service ought to orientate itself towards answering the questions of unbelievers according to their terms, while the answers are however not soft-pedaled.
The key question is whether the passages Keller cites actually support his idea of "evangelistic worship." I suggest they do not. The first passage, 1 Corinthians 14:24-25, speaks of what happens when unbelievers are in a worship service. Keller is right in his approval of what the commentaries say. But it is a logical leap to go from saying that the proclaiming of God's Word (which in the canonical era is partly expressed in prophecy) in the church service would lead unbelievers present to conviction of sin, repentance and faith, to saying that therefore service ought to be oriented towards evangelism in the "seeker-sensible" fashion. The first does not imply the second. What 1 Corinthians 14:25-25 teaches is that we should expect unbelievers to be present and we should proclaim God's word and the Gospel such that they might repent of their sins and turn to Christ in faith. It says nothing about whether we should alter the church service to make it more catered to the forms and terms (but not content) of unbelievers in the name of evangelism.
Keller's interpretation of Acts 2 is even worse. Acts 2 began as a prayer meeting, but when the Spirit descends at Pentecost, it did not become a worship service. Pentecost is a distinct sign, a unique event in the history of salvation. Keller is thus wrong in identifying Pentecost as a worship service. Therefore, that the sign attracts outsiders is not surprising, since that is what a sign is supposed to do — attract attention so that it may point to the reality God intends to reveal.
If Keller was just arguing about thinking of unbelievers and not using unnecessary Christianese, there would be nothing worth disputing. And on that, it is true that many churches could probably do better in making sure unbelievers who may visit know what is going on during the service, and also make the Gospel message more explicit. But being comprehensible in this sense is not the same as being "comprehensible" in Keller's sense. We should embrace the former, while rejecting the latter.