At the 2014 General Assembly, two UUPA members moved to include the category of "family and relationship structures" in the UUA's nondiscrimination rule, along with other amendments; the package of proposed amendments was ratified by the GA delegates.
Bigamy is the act of marrying one person while already being married to another, and is legally prohibited in most countries in which monogamy is the cultural norm.
In many jurisdictions where same-sex couples can access civil unions or registered partnerships, these are often intended as parallel institutions to that of heterosexual monogamous marriage.
Swingers and polyamorous people alike might engage in secret infidelities, though this is no more acceptable than in monogamy.
"Polygamy" generally refers to codified forms of multiple marriage (especially those with a traditional/religious basis), while "polyamory" implies a relationship defined by negotiation between its members, rather than by cultural norms.
A person with polyamorous relationships may also engage in swinging and other open relationships.
As well, swingers occasionally develop deep emotional attachments with their sexual friends.