Ketubot 14B

שמעתי, כל שאין בה אחד מכל אלו ⁠— משיאין לכהונה.

I heard that with regard to the widow of any family that has none of these uncertainties associated with it, one allows her to marry members of the priesthood. The only uncertainty where this ruling applies is in the case of uncertain ḥalal status.

רבי שמעון בן אלעזר אומר משום רבי מאיר, וכן היה רבי שמעון בן מנסיא אומר כדבריו: איזוהי אלמנת עיסה ⁠— כל שנטמע בה ספק חלל.

R' Shimon ben Elazar says in the name of R' Meir, and likewise R' Shimon ben Menasya would say in accordance with his statement: Who is the widow whose late husband was a member of a priestly family of questionable lineage? It is a widow who marries into any family in which a person with regard to whom there is uncertainty whether or not he is a ḥalal was assimilated among its members. Therefore, she is referred to as a widow of dough [issa]. Just as dough is the result of a mixture of several ingredients, this family too has a person with regard to whom there is uncertainty whether he is a ḥalal mixed within it.

מכירין ישראל ממזרים שביניהם, ואין מכירין חללין שביניהם.

The reason for the distinction between uncertain ḥalal status and uncertain mamzer status is that Jews identify the mamzerim that are among them, and there is no concern lest they assimilate into families of unflawed lineage. But they do not identify the ḥalalin among them. Therefore, there is concern lest a ḥalal assimilate into the family.

אמר מר: איזוהי אלמנת עיסה ⁠— כל שאין בה לא משום ממזרות, ולא משום נתינות, ולא משום עבדי מלכים. הא חלל ⁠— כשר.

The Talmud analyzes the baraita. The Master said in the baraita: Who is the widow whose late husband was a member of a priestly family of questionable lineage? It is one who married into any family that does not have the status of being unfit, neither due to uncertain mamzer status, nor due to uncertain Gibeonite status, nor due to uncertain status as slaves of kings. The Talmud infers: However, if it is due to uncertain ḥalal status, her marriage to a priest is deemed fit.