The issues of believing in the divinity have been already addressed many times, especially by Bakunin.
First of all, the belief puts man in a position of inferiority and subordination to a fantastic being on behalf of which men oppose themselves to other beliefs. And this is the first and most inconsistent of all the foulness of the institutional religions with anarchist thought.
Secondly, as described beautifully by Schopenhauer: either you think or you believe. And anarchism is based in turn precisely on the rational and anti-dogmatic feeling which allows the dynamism necessary for a free society.
Furthermore institutionalized religion proceeds by inviolable dogmas, namely it moves from a few thousand years old crystallized vision of life which rejects the calling into question of its assumptions and the acquisition of new experiences and knowledge. In some cases religion goes as far as to deny science (indoctrinating children), as in the case of creationism or AIDS.
The ethical problem of religion is that people are not driven to achieve their best. In other words, someone who follows the prohibitions of the church is simply avoiding to be a criminal and not acting as a positive influence on the world. Indeed the very idea of hell contradicts that of free will. On the other side, while the religious prohibitions are insufficient (prohibitions only determine the absolute limit of evil that a society is willing to tolerate), the rational ethics can lead to a fully realized ethical life.
Notwithstanding that the anarchists are not really in opposition to individual belief but rather to the authoritarian and deceitful nature of organized religion, those institutions are mostly hierarchically organized, and very often, in close alliance with the State and capital (as happened for the major fascists coups in Italy, Spain and South America).
Among other things religions usually prescribe certain rules in an authoritarian way, as seclusion or celibacy, that are incompatible with individual freedom promoted by anarchism.
In short, religion has always been seen by Marxism and anarchism as the opium of the people, or rather something functional to the coercive power of the bosses to which the faithful are subject loyally and obediently as much as they kneel to their god (religion puts man in the position of having to save his soul and earn the forgiveness of God rather than seize a decent way of life, and it calls for the submission to the pain, suffering and sacrifice because part of the misleading earthly life).
Some people think that these two things are not so opposed as some might think (one of the classic anarchist slogan is: No god, no master). There is even a christian inspired libertarian movement started from Tolstoj, but with deep roots in the tradition of the heretics, the Anabaptists of Münster and the radical Christianity of the Diggers (Thomas More and Campanella utopias were christian books, and Liberation theology has played an important role in Latin America socialism).
Anarcho-christians going back to the mythologized figure of Christ (regarded as the first true anarchist), claim to be able to recreate the kingdom of heaven on earth. In any case, the key thing is that they do not rely on the irrationality of religion, but derive from it lessons to be applied in a rational way.
Religion tends to conceive a genuine relationship with God in the observance of obsolete rites. Spirituality tends to replace the relationship with God with the connection with the real (natural) world. It is an overcoming of false hopes, meaning the re-appropriation of the present time and the discovery of the new possibilities of material life to live in an increasingly less material way. Spirituality is the search for understanding of life and the universe, the search for a higher consciousness, the union with others and return to nature.
And to me it is exactly this constant spiritual quest the foundation of anarchism and the reason why religion and spirituality (as well as religion and anarchism) are incompatible.