Here is an insightful take on Evangelization and how to bring people to God. Matt Nelson discusses the causes and types of indifference and how to initiate a conversation with the indifferent. Here is his take on the indifferent:
Closed Indifference: The closed minded indifferent believes that the existence of God is ridiculous. Science, in their view, proves that nothing exists but the material world. That view is a philosophy called 'materialism', not really science. So, in the view of the materialist, if nothing but 'material things' exist, there is no point in discussing God, faith or religion. Their minds are closed to even the possibility of God's existence.
Open minded Indifference: Basically, the problem is relativism; the belief that the only principle that is true is that there is no truth, at least not a truth we can know with certainty. The only exception to this radical openness is the basic orientation that no matter what is said, a true seeker of truth must keep an open mind to other points of view. Commitments to a way of believing other than relativism itself is avoided. The open minded indifferent is free from commitment to any God that makes a demand on the believer. G.K. Chesterton said that an open mind is like an open mouth; it should be closed on something solid. The open minded indifferent are open to a conversation about faith, but their basic commitment is to keep an open mind, keep seeking and not commit to something other than openness itself.
Denominational Indifference: Basically, the problem is relativism again. The denominationally indifferent believe that it doesn't matter what your religious beliefs are, as long as you believe in something. If all religions are equally true, why be a Catholic? The denominational indifferent believe that there are many paths to God including Buddha, Mohammed, various spiritual teachers and being good. Jesus is just one more teacher and was a good man, but isn't God anymore than the rest of us.
How to respond to the indifferent? Listen to Dr. Nelson discuss religious indifferentism.