Q. If a rabbi’s interpretation is overruled by a Beth Din or a world-renowned halachic authority, does the rabbi have to resign?
A. Only if the rabbi makes a decision that is, God forbid, blatantly contrary to the law would there be any thought of resigning.
On most things, there will be differing interpretations which cannot all be right. An example is an ancient debate about a verse that comes three times in the Torah, “Do not boil a kid in its mother’s milk”. The final answer to what “mother’s milk” means is any milk, but Rabbi Yose the Galilean thought it applied only to mammals which literally have “mother’s milk”. As a result of this view, poultry in milk was permitted in his township in Talmudic times. Rabbi Yose the Galilean was overruled by the halachah, though no-one questions his sincerity and piety.
It is part of the democracy of discussion that sometimes your view prevails and sometimes it doesn’t. Start with the first paragraph of the Mishnah and you already see that there were differing interpretations. Those whose views were rejected would have rejoiced to see the vibrancy and sincerity of the scholars involved in the thrust and parry of the debate.