Yoma 7A

דכל טומאת מת בציבור רחמנא שרייה.

as in all situations of impurity imparted by corpses in cases involving the public, God permits those who are impure to perform the Temple service.

אמר רב ששת: מנא אמינא לה, דתניא: היה עומד ומקריב מנחת העומר ונטמאת בידו, אומר ומביאין אחרת תחתיה. ואם אין שם אלא היא, אומרין לו: הוי פקח ושתוק.

The Talmud analyzes the rationale behind the two opinions. Rav Sheshet said: From where do I derive to say that impurity is overridden in cases involving the public? It is as it was taught in a baraita: If a priest was standing and sacrificing the omer meal-offering and it became impure in his hand, the priest, who was aware of what transpired, says that it is impure and the priests bring another meal-offering in its stead. And if the meal-offering in his hand is the only meal-offering available there, the other priests say to him: Be shrewd and keep silent; do not tell anyone that it is impure.

קתני מיהת אומר ומביאין אחרת תחתיה! אמר רב נחמן: מודינא היכא דאיכא שיריים לאכילה.

In any case, it is teaching that he says that it is impure and the priests bring another meal-offering in its place. Apparently, when it is possible to perform the service in a state of purity, even in cases involving the public, it is preferable to do so, and the prohibition of ritual impurity is not permitted. Rav Naḥman rejected the proof and said: I concede that in a case where there are remnants of the offering designated for eating it must be performed in purity wherever possible. Although it is permitted to sacrifice an offering when impure, the mitzva to eat portions of the offering must be performed in a state of purity. Therefore, in cases where portions of the offering are eaten, the preference is to sacrifice the offering in a state of purity.