Hillary Clinton doesn't say much to the evangelicals one way or the other. She knows she won't get any votes from them because they are ultra-conservative, and they regard her and her husband as incarnations of evil. Don't ask me why. Obama doesn't have anything to do with them either, for much the same reasons.
Her nomination wouldn't move the Democratic party to the right, left, or much of anywhere on "moral values," because her views are pretty much in sync on them with what the majority of Democrats favor. Her election would definitely move them to the left of what they are now.
That last sentence should have read that her election would move the White House to the left of where it is now.