Spielberg was inviting the audience to explore spirituality. And, to not fear it. Heroes now jump toward the light on a regular basis now. Doves are a standard in John Woo films. I am a Christian.
Doves represent the purity of love, beauty.
Also the dove is a messenger between people and God. Ride 'em cowboy. This is pure old western movie posturing. For a film that really underlines this evolving continuum, see 'Easy Rider'. Our messianic archetypes, Ethan and Nyah save the world from its apocalypse.