Do the Shakers permit same-sex marriage?

No, but not for the reason you think. Members of the United Society of Believers in Christ's Second Appearing, known as the Shakers, are required to remain celibate. That means no marrying for anyone and no childbearing. Through attrition, the size of the church has fallen off somewhat, from 6,000 in 1840 to only 5 in 2009. All 5 remaining Shakers are committed to celibacy, so the question of same-sex marriage among them is academic.