Trevin Wax has written a clear, simple, and charitable introduction to a debate about the nature and boundaries of the kinds of Christian activities that validly should be called "mission." In brief: Should we use a broad definition, where "mission" encompasses all the various purposes which God calls Christians and the church in general to perform, e.g. being ethical at work; general acts of care and charity; standing against systematic oppression and working towards justice instead? If so, "evangelism" is only one part of the church's mission - a central, necessary, and irreplaceable part, but only one part nonetheless. The latter kinds of activities don't save anyone for eternity, but they do genuine good in this world which please God. And that kind of good makes a real difference in many parts of the world which have not benefited from the kind of Christian moral transformation which the West benefited from - the kind of moral transformation...
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A couple of great example of this worldview you've outlined come to mind:
1) Back in 2004, the Good Weekend magazine published an article with the title "I don't want to die a virgin" by Catherine Von Ruhland(we looked at it in apologetics, so I've got a hard copy, but I haven't been able to find a version of it on the web). The author was then a 40 year-old woman who was leaving evangelical Christianity for the reasons expressed in the title. Sadly, she'd fallen for that worldview hook, line & sinker.
2) This worldview also shows up in popular books on Jesus like the Da Vinci Code & The Holy Blood and the Holy Grail. As a young Christian, I was lent a copy of the latter book by my year's atheist and reading that Christians had to admit that Jesus must have had sex. For sex, their argument went, is an essential part of being truly human.