The radicalism of the Quakers, or the Religious Society of Friends, which led them to challenge many well established societal norms, bred suspicion among the rest of the Christian population. Quakers believed, and continue to believe, that God is revealed through 'inner light' which surpasses all religious scripture and church teachings. This had the anarchic implication that Quakers were not obliged to conform to any earthy legal system, - not helped by the fact that Quakers tended to withdraw from secular social life - an idea which could threaten to undermine the basis of the fledgling and fragile colonial society. In addition to refusing to conform to some of the most fundamental doctrines and practices of the Christian faith, Quakers challenged other societal taboos by encouraging women to preach. Practically from the moment of their arrival in the New World, Quakers' were determined to spread their radical message, often by disrupting social meetings, which was not very well appreciated, especially when their message was seen as a threat to the very fabric of society. To understand why their message was seen as such a threat, one must consider the impact of the English Civil War on the public consciousness. Amidst the chaos of the War, dissenting religious groups, such as the Quakers, flourished unchallenged by the established Church of England. One product of this febrile intellectual climate was 'Antinomianism', which parented other radical groups such as the Ranters. Antinomianism was based upon the same premise as Quakerism, that the divine was revealed principally through 'inner light', but explicitly stated that all forms of law, secular and religious, were redundant. Antinomians often expressed their liberation from the law by drinking excessively, having lots of sex and generally causing a nuisance. Quakerism was therefore inseparably associated with these disruptive and radical groups, as well as the intense instability of the English Civil War.

EDIT: Some books worth reading on the matter:

A History of Christianity - Diarmaid MacCuloch

The World Turned Upside Down: Radical Ideas During the English Revolution - Christopher Hill