Why should we listen to mitzvos dirabanan?
You are asking an important question, as many people have misunderstandings about this.
The reason why we must do mitzvos d’rabonon, is because essentially it is a mitzva d’orayso to do so. Hashem told us in His Torah (Devorim 17-11) על פי התורה אשר יורוך ועל המשפט אשר יאמרו לך תעשה לא תסור מן הדבר אשר יגידו לך ימין ושמאל: “According to the instruction that they will teach you, (referring to the great Bais Din) and according to the laws that will tell you, you should do, do not stray from what they say right or left”. The Ramban on that verse says that even let’s say they made a mistake, we should still listen to them, because that is the mitzva. This we see from the Mishna in Rosh Hashana that R’ Yehoshua came to R’ Gamliel on the day that according to him would have been Yom Kippur, and he desecrated Yom Kippur according to his calculation, because the Nassi said that Yom Kippur is on a different day. The reason this is so, is because the Torah gave the jurisdiction to the Rabonon, and now their word is like we were commanded to do so from Hashem.
The Rambam (Hilchos Mamrim 1-2, and Sefer Hachinuch (Mitzva 495) say that his includes whatever chazal say that they had from tradition from Moshe Rabeinu, it also includes whatever chazal learned from the torah via the “13 middos”, and it also includes whatever safeguards that chazal instituted.
Included in this are even the things that our gedolim tell us. As the Sefer Hachinuch writes “Included in this mitzva is to listen to the judges of each time and generation, as our sages wrote, (Rosh Hashana 25b) “and listen to the judges that will be in those days” Yivtach in his generation was like Shmuel in his generation”. Meaning that we are commanded to listen to the words of Yivtach in his generation, the same way we listened to Shmuel in his generation (although he wasn’t as big as Shmuel was). And one who violates this and does not listen to the words of the sages violates this commandment, and his punishment is great, because this (mitzva) is the supporting pole that the torah rests upon, as is known to anyone who has daas.”