The real issue relating to exclusiveness is whether or not the Christian actually has a relationship with God, a presence of God, which non-Christians do not have. Apart from Christian spiritual formation as described here, I believe there is little value in claiming exclusiveness for the Christian way.
Dallas WillardThe revolution of Jesus is in the first place and continuously a revolution of the human heart or spirit...it is a revolution of character which proceeds by changing people from the inside through ongoing personal relationship to God in Christ and to one another. It is one that changes their ideas, beliefs, feelings, and habits of choice, as well as their bodily tendencies and social relations. It penetrates to the deepest layer of their soul. External, social arrangements may be used to this end, but they are not the end, nor are they a fundamental part of the means
Dallas WillardFeelings too must be renovated: old ones removed in many cases, or at least thoroughly modified, and new ones installed or at least heightened into a new prominence.
Dallas Willard