Why is it, that if one were to follow Beis Shamai's halachic opinions, he'd be obligated to the death penalty, as we see the Gemara in Brachos 11a says that:
רב נחמן בר יצחק אמר עשה כדברי בית שמאי חייב מיתה דתנן אמר רבי טרפון אני הייתי בא בדרך והטתי לקרות כדברי בית שמאי וסכנתי בעצמי מפני הלסטים אמרו לו כדאי היית לחוב בעצמך שעברת על דברי בית הלל:
Rav Naḥman bar Yitzḥak stated an even more extreme opinion: One who acted in accordance with the opinion of Beit Shammai has acted so egregiously that he is liable to receive the death penalty, as we learned in our mishna that Rabbi Tarfon said to his colleagues: Once, I was coming on the road when I stopped and reclined to recite Shema in accordance with the statement of Beit Shammai. Yet in so doing, I endangered myself due to the highwaymen who accost travelers. The Sages said to him: You deserved to be in a position where you were liable to pay with your life, as you transgressed the statement of Beit Hillel.