Niddah, Chapter 4, Mishnah 3. Before we can understand this Mishnah, one halacha has to be clear. Any blood that comes from a woman's womb makes her a niddah, and her age is irrelevant: even a baby girl lying in her cradle is included, and everything she touches or sits upon contracts tumah mishum niddah. While the Beis Hamikdash still stood, Jewish households took this seriously, keeping an eye on their little girls and relating to any blood that appeared as dam niddah. But there were circles that did not maintain this level of care, and the girls born into them must consequently be regarded mi'safek as niddos from the time they are infants. The Mishnah before ours applied that ruling to the daughters of the Kussim; here the Mishnah takes up the daughters of the Tzedukim.
Following in their fathers' footsteps
The Mishnah states: "Bnos Tzedukim, bizman shenahagu laleches b'darchei avoseihen, harei hein keKussiyos." The Tzedukim were Jews, not converts, but they were not careful in Torah and mitzvos. They had developed an entire system of lenient readings of Torah Shebichsav, and they rejected Torah Shebe'al Peh. As long as the daughters of the Tzedukim conduct themselves according to the ways of their forefathers, meaning that they are not careful in Torah and mitzvos, their halachic status is identical to that of the daughters of the Kussim, with all the dinim of a tumah mi'safek that come with it.
The Mishnah then adds: "Peirshu laleches b'darchei Yisroel, harei hein keYisroel." If they broke away from that path and began to conduct themselves as Jewish women do, they are treated as Jewish women in every respect. According to the Tanna Kamma, then, the burden of proof rests on these women: they must show that they have taken up darchei Yisroel.
Rabbi Yosei's view
Rabbi Yosei holds otherwise: "Le'olam hein keYisroel, ad sheyifreshu laleches b'darchei avoseihen." To his mind, our starting point is that they are Jewish women in every sense, and that assessment shifts only once something indicates that they have taken up the errant practices of their fathers. Rabbi Yosei thus asks nothing of these women; we judge them favorably as women who live as Jews and keep Torah and mitzvos, so long as nothing we see points the other way.
The halacha
The halacha is in accordance with the Tanna Kamma. A daughter of the Tzedukim is presumed to be walking still in the practices of her family, and she is not presumed to have taken on the conduct of Klal Yisroel. Only once she shows that she has moved over to darchei Yisroel is she given the status of a Jewish woman in these halachos.