[ Ed.: I generally try to avoid religious discussions here, but please excuse me this once as I get a bit philosophical... ]
Issues like gay marriage and abortion are sensitive because they are moral questions and thus inherently subjective. If everyone has a different set of values and belief systems, how can we trust the decision of one group over another? Sure, there are things we can all agree on - murder is bad - but there's plenty we can't.
For example: As a Christian, I am against abortion because it's wrong based on my beliefs - BUT, I am vehemently pro-choice. It would, after all, be incredibly arrogant for me to think that my decision is right for everyone.
Speaking of faith, one of the standard responses with many of these issues is an appeal to the founding fathers' religious beliefs. "This nation was founded on Christianity", they tell me.
A good write-up in The Week awhile back back discusses the faith of the framers in depth.
The faith that many of the Founders embraced was deism. Less a religion than a way of perceiving divinity in the world, deism is rooted in the 17th- and 18th-century scientific and philosophical revolutions of the Enlightenment. For deists, God is not a father figure who dwells in heaven and performs miracles. Rather, he is an undefined and unknowable “prime mover” who reveals himself in immutable laws that can rationally explain both cosmic and human affairs. Everything from the physical forces that govern the universe to the essential freedom of man, deists believe, are outward signs of God’s presence among us. In keeping with their deist beliefs, the Founders often refrained from calling the source of their inspiration “God.” He—or, rather, it—was “Divine Providence” and “The Universal Sovereign,” among other euphemisms.
Religion is a man-made construct - an attempt to understand something so abstract that it otherwise falls well beyond our understanding.