“Philosophy is the goal toward which religion was only a helplessly blind groping. The grandeur, the reverence, the exalted purity, the austere dedication to the pursuit of truth, which are commonly associated with religion, should properly belong to the field of philosophy.” — AYN RAND 
Religion affirms the supernatural, faith, and altruism leading to theocracy
Religion is a pre-philosophical outlook of the world (that attempts to provide a comprehensive view of existence) that affirms the supernatural, faith, and altruism.
In metaphysics, religions such as Christianity, affirm the supernatural and miracles (as opposed to the natural and causality), in epistemology religion declares revelation and faith as one’s means of knowledge and grasping truth (as opposed to reason and logic), in ethics religion preaches self-sacrifice of altruism (as opposed to the selfishness of pursuing one’s happiness).
The result of such a religious outlook is in principle identical to the “Materialistic mysticism” of Marxist atheists: some form of statism that denies the rationality of the individual human mind to justify the altruistic theory of self-sacrifice for the “greater good.” (In the case of atheistic statists they intellectually substitute society for god, though the effects are the same).
The political system based on religion is as a theocracy (theos being the greek word for god.)
Capitalism depends on the natural, reason, and self-interest (the pursuit of happiness)
The philosophical case for capitalism is based on the recognition of the primacy of reality (“A is A”), the acceptance of reason as an individual’s only means of objectively knowing reality (“reason as an absolute”), and the preservation of human existence requires the pursuit of one’s rational self-interest. To these three pillars, religion as a fundamental belief system stands, in principle, opposed.
This is not to say that the religions of the world, do not have some good (rational) advice to offer (albeit on a contradictory, mystical base), but in terms of fundamentals to the extent that a religious doctrine is actually religious (irrational, based on faith), it is destructive of human life and all it depends upon. 
Notes & References
 Ayn Rand, “The Chickens’ Homecoming” Return of the Primitive: The Anti-Industrial Revolution 46
 Comments Ayn Rand on this issue in a Playboy Interview (March 1964):
PLAYBOY: Has no religion, in your estimation, ever offered anything of constructive value to human life?
RAND: Qua religion, no — in the sense of blind belief, belief unsupported by, or contrary to, the facts of reality and the conclusions of reason. Faith, as such, is extremely detrimental to human life: it is the negation of reason. But you must remember that religion is an early form of philosophy, that the first attempts to explain the universe, to give a coherent frame of reference to man’s life and a code of moral values, were made by religion, before men graduated or developed enough to have philosophy. And, as philosophies, some religions have very valuable moral points. They may have a good influence or proper principles to inculcate, but in a very contradictory context and, on a very — how should I say it? — dangerous or malevolent base: on the ground of faith.
For further study:
“Religion vs. America” by Leonard Peikoff
In this 1986 lecture given at the Ford Hall Forum, Dr. Peikoff discusses the profound irreconcilability between religion and the pro-reason philosophy upon which America was founded.