I agree that you share the same values with this woman and this particular disagreement could be an example of a different perceptions rather than weighting of values. I assume that she values fairness but feels ambivalence over the issue, worrying that gay marriage violates her values of tradition and sanctity. I feel no such ambivalence and I bet you don't either, arguably because we don't perceive gay marriage as violating the value of sanctity.
But a lot of other political disagreements do boil down to value priorities. The health care debate involved a lot of harm reduction vs. individualism. I assume that most Americans value both, but you could reliably predict support or opposition to Obamacare based on which they prioritized.