Effective intercultural communication must become personal to the receptor.
Theologically speaking, God sent his Son, Jesus, to personally interact with humanity that we might, by his example, learn to live and love as he did (c.f., Jn 13.12-20; 1 Pet 2.18-25). Jesus, being God in the flesh, gave us an example by becoming like us and transcending all cultures for all times through this means (though Jesus as example here is by NO means the only reason for the incarnation). As John says in his gospel, “And the Word became flesh and dwelt among us” (Jn 1.14a). God communicated and continues to communicate to us and the world through his Word, the Son of God (c.f., Heb 1.1-3). God has ordained the means of communicating to his world in his Son, that we might know him, love him, and love our neighbor (both locally and globally) by incarnating Christ with our lives and proclaiming Christ, lovingly with our mouths.
For example, we might engage a culture through telling the grand biblical story of God’s faithful work of redemption from Creation to the renewal of Creation. Or, more concretely, we may need to take on tent-making roles so that our presence and interaction with the culture makes sense to the natives and is mutually beneficial and teachable from both perceptions. When the apostle Paul stood in Athens (Acts 17), he engaged well with the Greek culture because he had already immersed himself in their own philosophical and poetic writings. We would do well to imitate Paul in this way, by walking into the world of the unbeliever (or, in other cases, realizing we presently live in their world): their world of literature, visual media, and audio media, that we may know what particular questions they are asking (a la Francis Schaeffer). For Paul himself said, “I have become all things to all people, that by all means I might save some” (1 Cor 9.22b). And, Paul calls all Christians everywhere to become personal to their receptors, as he himself did: “Be imitators of me, as I am of Christ” (1 Cor 11.1).