This is an interesting assertion. Reading through the Bible, a lot of those whom we'd consider faithful nevertheless questioned God, wrote poems to lament his apparent absence, his allowance of injustice, etc. It seems that in a healthy relationship with God, God will do things we don't understand and we are expected to express questions and concerns to him. Why is the Bible above God in that sense?
Job and his friends, who were allowed to question God at length, before he gave his answers. Israel, whose name itself is a testimony to God's patience with our struggle. Abraham, who haggled with God at Sodom. Jesus himself, who prayed for another possibility. Etc., etc.
Don't get me wrong - this isn't the first time I've heard the claim. However, every time I hear it, I get the sense that the believer doesn't have a relationship with a living Person, in which there are necessarily misunderstandings and disagreements, but the believer is following the Bible as a constitution he hasn't really read.
Unquestionable? No. We might not agree with the answers, but the entire Bible invites question. In short, this sounds a lot like bibliolatry.
Everyone within earshot of the debate knows the Christian stance on gay marriage, civil unions, domestic partnerships, etc. You don't have to worry - there are millions being spent on making sure your message is overwhelmingly clear.
What you're witnessing is disagreement. The two are often confused, because if someone disagrees with me, it must be because they're confused, right? But no.