No, this is real. Liz was openly quoted as lenient toward lesbian “marriage” early on, for the sake of her sister, and does now have need, politically, to back away from it.
The parents openly supported it in the same vein, to the surprise of many, when it struck their family.
The Cheneys don’t strike me as particularly grounded in devotion to faith, but my bet is they do abhor the whole stinking gay/lesbian thing, feeling forced to support “equalty in marriage” for the sake of Mary. Ick.
I like Liz on policy, believing she is a dependable and intellegent conservative. Can she upset Enzi? Hope so.
The statements in your post tend to reinforce my initial suspicion that this is all a political ploy to back away from a prior position that she now feels could hurt her politically.