There were many time periods in Klal Yisrael, notably during the time of the second Beis Hamikdash and for some time afterwards, that the Minim were either in power or in positions where they could not be denied debate. As is apparent from the special Berachah "v'Lamalshinim" in Shemoneh Esrei, and the fact that the Gemara states that if someone stops and/or does not recite the Berachah it is a sign that they are a Min (Berachos 28b, 29a), they also often blended into religious society. Just as today it is difficult sometimes to classify certain people's level of religious observance, it was even more complicated when many people participated in davening, learning, etc. but yet held heretical views. This is why the Mishna in Yoma (ch. 1) tells us that the Kohen Gadol had to take an oath that he would do the Avodah of Yom Kippur according to the Torah, and not like the manner specified by the Tzedukim. The Gemara (ibid.) states "Don't believe in yourself until the day you die, because Yochanan Kohen Gadol served as Kohen Gadol for 80 years and ended up becoming a Tzeduki." This shows that there was much mixing between the Perushim (Torah-True Jews) and the Minim. Due to their power, Chazal had no choice but to try to win them over via debate. When they did, they would sometimes establish a Yom Tov (see Menachos 65a). For more information on this relationship, I suggest reading Artscroll's History of the Second Temple Era (I don't remember if that is the exact title).

All the best,

Yaakov Montrose