During the period of the Second Temple there were two main groups of Jews in Jerusalem, the Perushim and the Tzedokim. The Perushim were the Pharisees, the sages of the Talmud, while the Tzedokim were the Sadducees, the elite class that rejected many of the traditions of the Perushim.
The disagreements between the Sages of the Talmud and the Sadducees existed on a number of different levels, ranging from broad concept of faith, like the question of the existence of a World to Come, to practical issues of halakha where the Sadducees rejected the oral traditions of the Sages of the Talmud. Generally speaking, the Sadducees were among the elite population who had close relationships with the later Hasmonean kings, and they had significant political power, even as they were a minority of the population. Their attempts to create tension between the Sages and the monarchy led the Sages to publicly reject their positions, even when there may have been good reason to consider them.
The Mishna on today’s daf discusses the practices of the Tzedokim with regard to questions of ritual purity. The Tanna Kamma rules that we assume that the daughters of the Tzedokim follow in their father’s footsteps unless we know that they have begun to keep the laws according to the Sages; Rabbi Yosei argues that we only assume that they follow the ways of the Tzedokim if it is clear to us that they do so.
The Gemara relates:
It once happened that a Sadducee was conversing with a High Priest in the market place when some spittle was squirted from his mouth and fell on the clothes of the High Priest. The face of the High Priest turned green [he feared his garments had been made ritually impure] and he hurried to the Sadducee’s wife who assured him that although they were wives of Sadducees they showed respect to the Pharisees and showed their blood to the Sages when uncertainty arose [i.e. the Sadducee wives properly observe the of menstruation so the High Priest’s garments are still pure].
In his Commentary to the Mishna the Rambam rules like the Tanna Kamma, but he does not mention the discussion in his Mishneh Torah, perhaps because by this time the sect of the Tzedokim no longer existed.