Tefillin

Why, in your opinion, did the dispute over the order of writing the parshiot in tefillin, between Rashi and Rabbi Tam, "catch" in parts of the Jewish people, and they are careful to place according to both methods? Are there no halachic disputes in which it was possible to act according to both methods of the dispute? The first example that comes to mind is the dispute over the order of lighting the candles between Shammai and Hillel; we could have acted according to both methods – to light two menorahs, one increasing and one decreasing and one decreasing. (The Pirsuma Nissa is not based on the specific day of Hanukkah, so even if they were initially confused in determining the day – for someone who observes two menorahs – this would not have undermined the main purpose of the Pirsuma Nissa).