Evolution is an affront to young-Earth creationists because it conflicts with Biblical accounts of the origins of life and suggests that humans are animals, as opposed to beings made in God's divine image. But it's increasingly clear the case against evolution has also become entwined with opposition to gay marriage.
This is partially because the Book of Genesis contains passages that conservative Christians have cited as evidence that homosexuality and same-sex marriage are prohibited by the Bible. For instance, Genesis 19:5 is said to be proof that homosexuality led to God's destruction of Sodom and Gomorrah.
As such, young-Earth creationists such as Mark Looy at Answers in Genesis declare:
In ridiculing the first eleven chapters of Genesis through "science" (like evolution and millions of years), the secular world has managed to convince too many Christians that they don't have to accept biblical authority in Genesis regarding doctrine and institutions (like marriage, in Genesis 2). They have thus laid the groundwork for Christians not to accept scriptural authority in other sections of the Bible (e.g., in Leviticus 20:13, where homosexual behavior is condemned).
In the most recent issue of the Atlantic, Jeffrey Goldberg writes about his own visit to Ken Ham's $35 million Creation Museum in Kentucky, and was surprised by how quickly the conversation turned to gay marriage:
Sitting with Ken Ham and Terry Mortenson, a historian of geology and a theologian on staff, I asked why it is so important to convince their visitors—more than 2 million since the museum opened seven years ago—that Genesis is a book of history. "There's a slippery slope in regard to authority," Ham replied. "If you say that the history in Genesis is not true, then you can just take man's ideas as true. When you go outside of Scripture, why shouldn't you just reinterpret what marriage means? So our emphasis is on the slippery slope regarding authority."
"Show me another book in the world that claims to be the word of one who knows everything, who has always been there, that tells us the origin of time, matter, space, the origin of the Earth, the origin of water, the origin of the sun, moon, and stars, the origin of dry land, the origin of plants, the origin of animals, the origin of marriage, of death and sin," he said.
"Lord of the Rings?," I answered, tepidly.
"Well, there's no book so specific as the Bible," he said.
Mortenson stayed on the subject of gay marriage. "The homosexual issue flows from this. Genesis says that God created marriage between one man and one woman. He didn't create it between two men, or two women, or two men and one woman, or three men and one woman, or two women and one man, or three women and one man. If other parts of Genesis aren't true, then how could this idea of marriage be true? If there were no Adam and Eve and we're all evolved from apelike ancestors and there's homosexuality in the animal world and if Genesis is mythology, then you can justify any behavior you want."
"I found this preoccupation with gay marriage significant," Goldberg reflected afterwards, "because it suggests that perhaps at least some of those who profess a belief in creationism might simply be signaling their preference for a more traditional social order, rather than a rejection of modern science and free intellectual inquiry."