Rejection of transubstantiation (and, except by Lutherans, of consubstantiation).
Rejection of Purgatory, the Treasury of Merits, and indulgences.
Protestants differed on forms of church government:
Some argued for the autonomy of individual congregations; these were Congregationalists or Independents (1604-); more radical still were Brownists/ Separatists (1580-)
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Some wanted church government locally to be run by presbyters (pastors or ministers; elected for life), and elders (elected for short terms); pastors and elders were in turn to elect members of a regionalcouncil or synod; and the regional synod was to elect members of a national synod;
This system was Presbyterianism;
It would have taken power over the church away from the state.
Executions for heresy were rare after the death of Mary, but they did sometimes happen under Elizabeth and there were two final executions under James I (Legatt and Wightman; 1612).
Anti-Trinitarians were especially likely to suffer as heretics; in 1655 Cromwell sent the Socinian John Biddle into exile to save him from execution by parliament.
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In 1666, the philosopher and political thinker Thomas Hobbes was threatened by parliament with punishment for heresy (Great Fire of London 1666; the number of the Beast – in Revelation – is 666); he held unorthodox views on the Trinity and was thought to be an atheist (/Deist).
John Locke (philosopher) and Sir Isaac Newton (scientist) also held unorthodox views on the Trinity.
Overt atheism was dangerous; Christopher Marlowe was accused of it.