The story is told of a Torah scholar who was shopping in the supermarket on Erev Shabbat when a man approached him and commented that it was beneath the Rabbi's dignity to go shopping in the supermarket like everybody else. This kind of chore, the man claimed, should be assigned to a family member or student, rather than be done by the scholar himself. He proved his case from the Halacha exempting a Torah scholar from the obligation of Hashavat Aveida (returning a lost item to its owner) in situations where carrying the item to its owner would be beneath the scholar's dignity. This demonstrates that even in the performance of a Mitzva, a Rabbi must refrain from any activity that infringes upon his honor.
Was this man correct, or is it permissible for a Torah scholar to shop for food and drinks for Shabbat, given that this entails a Mitzva?
The Chavot Yair (Rabbi Yair Bachrach, Germany, 17th century) addresses a similar question, whether a Rabbi who plays a violin may join an orchestra at a wedding for the purpose of Simchat Chatan Ve'kala (celebrating with the bride and groom). Would we deem his participation in an orchestra inappropriate and an infringement upon his honor and stature, or would this be permissible given the fact that playing music at a wedding fulfills a Mitzva?
The Chavot Yair responded that this issue lies at the heart of an exchange between King David and his wife, Michal, after David escorted the Aron (ark) to Jerusalem with intense joy and dancing (Shemuel II 6:20-22). Michal criticized her husband's conduct, claiming that it was beneath his dignity as a king and righteous man. David, however, responded that to the contrary, performing this Mitzva of celebrating with the Aron is the greatest honor he could ever bring to himself. Accordingly, the Chavot Yair ruled that a scholar may perform a Mitzva even if it entails an action that would normally be beneath his dignity, as there is no greater honor than performing a Mitzva and thereby bringing honor to the Almighty.
Why, then, does Halacha exempt a Torah scholar from returning a lost item in cases where this would be undignified?
The Chavot Yair explained that in the case of Hashavat Aveida, people who see the Rabbi carrying the lost item are unaware that he is involved in the performance of a Mitzva, and therefore this would indeed infringe upon the honor of the Torah which he represents. In the case of the violin, however, everybody immediately recognizes that the Rabbi performs a Mitzva by playing music for a bride and groom, and therefore doing so brings him honor, and in no way is deemed beneath his dignity.
Similarly, a Rabbi shopping for food items in a supermarket on Friday morning clearly does so for the honor of Shabbat, which constitutes a Mitzva. It is therefore entirely permissible for a Torah scholar to go shopping for Shabbat, and we would not consider this an infringement upon his honor. This is indeed the ruling of the Bei'ur Halacha (commentary to the Shulchan Aruch by the "Chafetz Chayim," Rabbi Yisrael Meir Kagan, Lithuania, 1835-1933), in Siman 250. In this vein he explains the Shulchan Aruch's comment that one should take example from the Sages of the Talmud who would personally purchase delicacies for Shabbat, and one should not consider such a chore beneath his dignity, "for this is his honor – that he honors the Shabbat." Since shopping for Shabbat is very easily recognizable as a Mitzva act, a Rabbi need not be concerned about undermining his stature by involving himself in this activity.
This same principle applies to other Mitzvot, such as constructing a Ma'akeh (parapet) around one's roof, or building a Sukka. Although ordinarily we would consider construction beneath a Torah scholar's dignity, nevertheless, since these activities are easily discernible as Mitzvot, it is permissible for a Torah scholar to personally involve himself in these tasks.
Summary: A Rabbi may engage in an activity that would ordinarily be deemed beneath his dignity, if it is clearly recognizable as a Mitzva. Therefore, for example, a Rabbi may do Shabbat shopping on Erev Shabbat, play music at a wedding, construct a Ma'akeh around his rooftop and build a Sukka.
