Keiji Nishitani was a Japanese philosopher. His ideologies tended to parallel those of the Existentialists. Existentialists tended to believe that the experiences an individual had were the ones which molded said person into what, and who, he or she was. This idea was based upon the idea that "the identity of any one person—their essence—cannot be found by examining what other people are like, but only in what that particular person has done."
Therefore, the quote, "Those who question the need for religion are those who need religion the most," refers to his idea that one only questions something based upon their own lack of experience with it. Given that an individual, not society, rules how a person becomes who he or she is, one who fails to experience religion would question it. Therefore, in order to not question religion, the individual must possess some type of religious ideologies of his or her own.
Outside of this, Nishitani did not believe religion to be "how one worships," but more about "human meaning" and their "ultimate reality" (taken from eNotes "Religion and Nothingness" Summary). Therefore, the quote also refers to the idea that religion is important for all of mankind based upon one's complete understanding of his or her own existence in the world around them. In essence, an individual must have some type of religion in his or her life in order to realize why he or she exists in the first place.