Cumbey offered the first major criticism of the New Age movement from a Christian perspective in The Hidden Dangers of the Rainbow: The New Age Movement and Our Coming Age of Barbarism (1983), but quickly lost academic credibility due to her promotion of conspiracy theories linking the New Age movement to Benjamin Creme, theosophy and Nazism. Scholar of New Age religion James R. Lewis describes this book as containing "a few few insightful criticisms with many accusations of the least responsible sort", and that she is "simply lumping together anything that departs from a rather strict interpretation of Christianity." Cumbey's accusations include that the New Age movement has "infiltrated all of Christianity, as well as Judaism", and that it is the motivating force behind ecumenism, holistic health centers, New Thought, humanistic psychology, Montessori schools, modernism, secular humanism, and zero population growth. She states that Unitarian churches and health food stores become "New Age recruiting centers", that the Guardian Angels become one of the New Age movement's paramilitary organizations and that "the New Age Movement has complete identity with the programs of Hitler". Her contention is that the New Age movement is not simply expressing a naive or unscriptural interest in metaphysics, but that it is an organized conspiracy overthrow the United States and replace it with a Nazi-like regime.
Cumbey is harshly critical of all religions other than Christianity and Judaism, and those who take an interest in them.
While there are certain superficial similarities among most religions, orthodox Judaism and Christianity stand in direct opposition to every other belief system. It is safe to say, however, that nearly all non-Judeo-Christian religions are extremely similar because, as the Bible indicates, they come from one source, the 'god of this world'—Satan himself—Constance Cumbey, The Hidden Dangers of the Rainbow
In the wake of the attacks following the release of The Innocence of Muslims she suggested on her blog that the incident might have been a deliberate attempt by New Agers to set their enemies against one each other.
I have my own suspicions that this is an incited thing that is designed to set the three Alice Bailey delineated fundamentalist target groups of Jews, Christians, and Moslems off against each other. I have even uglier feelings that it was cynically produced and put in circulation with just that sort of "kill-off Monotheism" war... I suspect this may be a deliberate and well-financed move to incite the target groups against each other
- Is the antichrist in the world today? an interview with Constance Cumbey Oklahoma City: Southwest Radio Church 1982
- The New Age movement: age of Aquarius, age of antichrist. (Emil Gaverluk) and N W Hutchings) Oklahoma City: Southwest Radio Church 1982
- The Hidden Dangers of the Rainbow: The New Age Movement and our Coming Age of Barbarism Shreveport, La.: Huntington House, 1983
- A Planned Deception: The Staging of a New Age Messiah East Detroit, Mich: Pointe Publishers, 1986
- Lewis 1992, pp. 154–56
- Lewis, James R. (1996). Magical Religion and Modern Witchcraft. Albany: State University of New York Press. p. 344. ISBN 0-7914-2890-7.
- Fuller, Robert (1996). Naming the Antichrist. Oxford Oxfordshire: Oxford University Press. pp. 187–188. ISBN 0-19-510979-1.
- Tamney, Joseph (1992). The Resilience of Christianity in the Modern World. Albany: State University of New York Press. p. 113. ISBN 0-7914-0821-3.
- Irving Hexham, "The Evangelical Response to the New Age," in Perspectives on the New Age, James R. Lewis and J. Gordon Melton, eds., (Albany: State University of New York Press, 1992), pp. 152–163.
- Bob and Gretchen Passantino, Witch Hunt (Nashville: Thomas Nelson, 1990).
- John A. Saliba, Christian Responses to the New Age Movement: A Critical Assessment (London: Geoffrey Chapman, 1999).
- SCP Staff, "The Final Threat: Cosmic Conspiracy and end times speculation," in The New Age Rage, Karen Hoyt and J. Isamu Yamamoto, eds., (Old Tappan: Revell, 1987), pp. 185–201.
- The Constance Cumbey Papers at the Wayback Machine (archived December 8, 2005)
- What Constance thinks (blog)
- Constance Cumbey interviewed by GeorgeAnn Hughes of "The Byte Show"