A more fascinating situation is when a sect is accused of heresy over very subtle matters. For example, in the great schism between the Mitnagdim and the Chassidim, a major theological disagreement seemed to be the degree of G-d's immanence in the world. This seemed to be the crux of the GRA's famous letter to the Jewish communities in White Russia and the Ukraine.
This is similar in my mind to the great controversy in the Catholic church of the thirteenth century over the notion of Christ's poverty. Interestingly, while the Franciscan brotherhood preached poverty, it was not declared heretical, while other groups such as the Fraticelli and the Waldensians were.
Interestingly, in both cases, there were also secondary motivations for declaring the new groups heretical. both Chassidim and the Catholic poverty movements opposed elitism and endorsed power of the common people.