Moed Katan 14A

ומנודה שהתירו לו חכמים, וכן מי שנשאל לחכם והותר.

and one who had been ostracized and the rabbis released him from his decree of ostracism; and similarly, one who had vowed not to launder his clothes and he requested from a Sage to dissolve his vow and was released from it on the intermediate days of a Festival.

מטפחות הידים ומטפחות הספרים ומטפחות הספג, הזבין והזבות והנדות והיולדות, וכל העולין מטומאה לטהרה ⁠— הרי אלו מותרין. ושאר כל אדם אסורין.

Hand towels; and barbers’ towels, which are used to cover a person having a haircut; and body-drying towels, all of which get quickly soiled, may be laundered on the intermediate days of a Festival. Zavim, men suffering from an impure venereal emission; zavot, women who experience a flow of menstrual-type blood on 3 consecutive days during a time of the month when they do not expect to experience menstrual bleeding; menstruating women; women who have just given birth; and all others who leave a state of ritual impurity for a state of ritual purity on the intermediate days of the Festival, these people are all permitted to launder their clothes in order to purify themselves. But all other people are prohibited from laundering during the intermediate days of the Festival.

גמ׳ ושאר כל אדם מאי טעמא אסורין?

Talmud: The Talmud asks: What is the reason that all other people are prohibited from performing these actions during the intermediate days? Why are these actions not included in the category of actions that are permitted in deference to the Festival?

כדתנן: אנשי משמר ואנשי מעמד אסורין לספר ולכבס, ובחמישי מותרין מפני כבוד השבת.

The Talmud answers: As we learned in a Mishnah (Taanit 15b): Both the members of the priestly watch whose week it is to serve in the Temple and the members of the non-priestly watch who accompanied the members of the watch to Jerusalem are prohibited from cutting their hair or laundering their clothes during that week. But on the Thursday of that week they are permitted to do so in deference to Shabbat.