Ironically, religion in "Brave New World" has not been eradicated: it has been changed. When Mustapha Mond speaks to John the Savage, he mentions John Henry Cardinal Newman, an Anglican clergyman who later converted to Catholicism. He believed that man was not made for independence, but belongs to God. Mond claims that the New World takes this same concept and alters it to the new society in which God is not compatible with machinery, science, and happiness.
There is much observable truth to Newman's idea. People who are followers of a religion adhere to the principles, morals, and ideals of their religion. The New World cannot allow this religious dependency if it is to control its inhabitants. Therefore, the leaders of the New World replace religion with the Solidarity Service and the communion of soma. The sign of the T has replaced the sign of the cross. Religion has not truly disappeared; only the objects of veneration have. Just as Karl Marx wrote that religion was the opiate of the people and communism found a new opiate when it gained control, so, too, does the New World. It substitutes self-indulgence and soma as the opiate.
In a desire to create a "utopia" or some social experiment predicated on a collective vision of perfection, personal religion has to be removed. This is because the notion of collectivity roots itself in the idea that all of its citizens share the same emotional and political experience. When multiple paths to spirituality are granted, this experience makes individuals different, causing dissension, breaking the bonds of social collectivity and conformity in quite an intense manner. Religious devotion allows individuals to possess different emotional experiences, making frames of references diverse and eclectic. This is of nightmarish proportions for the designers of the perfect world, and this is evidenced in Brave New World. Ask yourself, in which moments in the book do we see a desire for people to have similar or shared experiences? My guess is that you can find many examples of this. The reason being that the shared experiences lend itself to a vision of collectivity. This is the driving force in the creation of all "ideal" societies. Religious faith punctures this vision because it creates multiple individual quests. The journey of the Hindu is vastly different than that of the person immersed in Judaic faith, whose experience might be different than the Buddhist. Each vision has different spiritual, psychological, and emotional calculations within this experience. Such nuances and divergent approaches make a singular vision of emotional and political experience impossible.
Where all of these narratives find a home is in the penchants of liberal democracy, a structure that can never aspire to social collectivity because of it. In a liberal democray, people are granted the freedom to pursue different paths, so long as it does not ostensibly detract from another's, and this is the vision of perfection. There is no other end outside of this individual expression, which is the diametric opposite of utopic visions and the world Huxley depicts.