Among organized religions, attitudes towards polyamory vary from extreme discomfort and distaste to complete acceptance. At one end of that spectrum, conservative or fundamentalist sects of Christianity, Islam, and Judaism abhor extra-marital sex and base family on a strident sexual exclusivity—for women. At the other end of the spectrum, Paganism and sacred sexuality of several varieties celebrate a multiplicity of gods and lovers. The more liberal and sex-positive a religion is, the more likely it will accept polyamorous relationships among its congregation.
The Big Three in the United States—Christianity, Islam, and Judaism—share the same theological foundations that mandate heterosexuality and marriage to create children. All three accept sexuality within religiously recognized unions and discourage extra- or non-marital sexuality, though Christianity tends to be more suspicious of sexual pleasure than either Judaism or Islam. None of the conservative sects of the Big Three encourage their adhereants to practice polyamory, in part because it allows women access to mutiple partners—something that is anathema to their religious tenets that require women's virginity at marriage and absolute sexual fidelity for the duration of their marriages.
At the most sex-negative end of the scale, some conservative forms of Christianity strictly prohibit sexuality for pleasure and mandate stark boundaries that confine sexuality to married heterosexuals who are trying to have children. Sex for fun is sinful, or at minimum immoral. Even though "The Book" (Torah/Old Testament) is filled with multiple-partner marriage, contemporary conservative forms of Christianity are stridently against non- or extra-marital sexuality (again, even though some of their most famous preachers have been caught in extramarital sexual relationships). All of the multi-partner relationships in the Book are polygynous—with one husband having multiple wives and lots of begatting. The non-monogamous past does not translate to contemporary acceptance, though, and in general most Christian sects are not known for their embrace of sexual diversity.
Some contemporary Christian-influenced non-monogamous groups practice polygyny, but explicitly reject polyamory becuase it allows women additional partners as well. For these Christians and fundamentalist members of the Church of the Latter Day Saints (FLDS or Fundamentalist Mormon), women are not supposed to have sex with any man other than her husband (of which she is allowed only one) and are not supposed to have sex with their husband's other wives—her "sisterwives"—either.
Generally Islamic beliefs are open to non-monogamous relationships, but only polygyny is acceptable. Muslim men are allowed to have up to four wives as long as the men are able to provide sufficiently for the women and children. Women, on the other hand, are mandated to strict sexual exclusivity with their husbands and can be killed for fornication/adultery known as Zina. While Islamic faiths also emphasize marital childbearing as the goal of sexuality, recreational sex between married people is acceptable and men must make sure to satisfy their wives’ sexual needs. Even with this more sex-positive view, the Islamic emphasis on women's pre-marital virginity and marital sexual fidelity makes it hostile to polyamory.
Judaism sees sexuality between married people as a mitzvah: a positive thing that varies from following a divine commandment to doing a good deed. This fundamentally optimistic view of sexuality differs markedly from the sex-negative view of conservative Christianity, and is much closer to Islamic beliefs that cast sexuality as an important part of sustaining companionship in a marital relationship, even beyond its function in childbearing. While Orthodox Judaism tends to be sexually conservative and require strict gender boundaries in social and religious interactions, Reform and Progressive Judaism both have more liberal atitudes towards sexuality are more likely to accept same-sex and other "alternative" relationships like polyamory.
Unitarian Universalism (UU)
Unitarian Universalism is the most liberal of the conventional religions and well known for its celebration of sexual and gender diversity. Joined as a faith community by their mutual desire for spiritual growth, UUs draw from many spiritual sources to find beliefs that emphasize freedom of personal faith, compassion, social justice, dignity, peace, respect, and personal responsibility. While one faction of the Unitarian Universalist Association (UUA) wants the religion to recognize polyamorous unions and include it in their educational materials, another is concerned that the specter of poly relationships looming at the end of the slippery slope will derail their beloved goal of same-sex marriage. Plus, it might make them look goofy to Jay Leno.
With sexuality, as in all things, Buddhism advises the Middle Way, meaning that people should be neither too hyper-sexual nor abstinent. Extremism of any sort breeds attachment, and attachment causes pain through loss, which is inevitable because everything is fleeting. Part of Buddhist belief includes refraining from wrong-doing in relationship to sexuality, and in general trying your best to use restraint.
Neither sin nor sacrement exist in Buddhism, so "Sexual indulgence is not wicked, but it may be in some degree inadvisable" because it encourages cravings and attachments. Marriage and relationships are civil matters in which people should use integrity. Polyamory, in this view, is neutral: It's impact is determined by how and why it is done. If polys (or anyone) act in ways that are motivated by attachment, then they are likely to experience loss. If they are able to use moderation and act responsibly with their multiple partners, then it is not morally wrong and can in fact be just fine when done with integrity.
With its multiplicity of faiths under one label and array of goddesses and gods within each faith, Paganism is unsurprisintly friendly towards polyamory. Like their more conventional counterpart the UUs, Pagans are a loose collection of people joined by their fundamental belief in an individual relationship with a divine presence, though exactly what that presence is or how it is embodied varies. People drawn to Paganism tend to be unconventional in other ways as well, and are generally open-minded (possibly even experimental) about sexual maters. Polyamory is so common among Pagans that it routinely passes unremarked in social settings.
Sacred sexualities are a collection of mystical spiritual traditions that use sexuality as a form of prayer and a pathway to worshiping the divine in each of us. Their emphasis on consciously constructed intimate connections expressed through sexuality resonates with the more esoteric poly crowd, and two forms are especially popular.
Tantra, a Sanskrit term that encompasses expansion, continuation, liberation, and union, is undoubtedly Eastern in origin, though whether Hindu, Buddhist, or a form of yoga remains in debate. A form of active meditation, the goal of Tantric sex is to allow participants to fully inhabit all parts of their own beings and recognize the divine in each other. While Tantra tends to emphasize heterosexual sex between two people, its sex-positivity and celebration of intimacy means that it is generally open to polyamorous relationships (at least in the US).
Quodoushka is a decidedly Western and recent amalgamation of Native American spiritual tenets combined to create a practice aimed to heal shame and allow spiritual seekers to experience the fullness of their intimate connections, though some critics dispute its reputed spiritual roots and see it rather as a money-making scheme. Sex-positive and constructed in direct opposition to shame, Quodoushka is friendly to polyamory.
Polys and Religion
Most of the people who responded to my study said they did not practice any religion, in part because poly's tend to be fairly suspicious of institutions, kind of anti-establishment folks a lot of the time. Of those who do practice a religion, the most popular are (in descending order): Paganism, Unitarian Universalism, Judaism, Buddhism, and some form of sacred serxuality. Paganism and polyamory just make sense together -- both are appealing to unconventional people and emphasize multiplicity. The UU lack of dogma and emphasis on peace and equality with personal choice fits perfectly with polyamory, which (at least attempts to) refuses dogma and celebrates freedom, honesty, and integrity. Buddhism, with its acceptance of fluidity and emphasis on integrity, is appealing to some of the more spiritual polys, while others see Tantric exercises as a great way to deal with jealousy.