Biblical sexuality and marriage in particular has become the modern day litmus test of inerrancy. Marriage is so intrinsically linked to the image of God, the authority of God and the gospel that to deny it is to deny the truth about God.
Marriage between one man and one woman, and sexual relations within that union, is God's idea, brought into existence by his Word in Genesis 2. Paul tells us that marriage was always pointing to the greater picture: Christ who died for his bride, the Church (Ephesians 5: 31-32). And this was foreshadowing the future glory of marriage: the Bridegroom coming to take his Bride forever (Revelation19). Affirming "same sex marriage" destroys that picture. But it is the fruit of denying the inerrancy of God's Word.
In other words, by the time a Church legitimizes "same sex marriage", it has already ceased to be a Church. The shift on a biblical idea of God and his Word has already happened and the result is a people who have created God in their own image, and whom he has given over to themselves so that they even approve of what is evil (Romans 1:32).