Heresy occurs when a person who is a baptised Christian obstinately denies or obstinately doubts any revealed truth that must be believed with the full assent of faith (also called theological assent, or a divine and catholic faith). The teachings that must be so believed are the infallible teachings of the Magisterium, whether taught under papal infallibility, or the infallibility of an Ecumenical Council, or the Universal Magisterium.
The non-infallible teachings of the Magisterium require the religious submission of will and intellect (also called religious assent). The obstinate denial or obstinate doubt of a non-infallible teaching is not heresy, but may be a lesser sin. Since non-infallible teachings admit a limited possibility of error, denial or doubt of such a teaching is not necessarily contrary to the virtue of faith.
Canon 751: “Heresy is the obstinate denial or obstinate doubt after the reception of baptism of some truth which is to be believed by divine and Catholic faith”
Canon 1364 §1: “an apostate from the faith, a heretic, or a schismatic incurs a latae sententiae [automatic] excommunication.”
Mere material heresy is the obstinate denial or obstinate doubt of an infallible teaching without the knowledge that the teaching is infallible, or that the idea is in fact a teaching. Mere material heresy does not excommunicate.
Formal heresy is the obstinate denial or obstinate doubt by a knowing choice. All acts of formal heresy inherently automatically excommunicate the offender. By the very nature of the sin itself, apostasy, heresy, and schism excommuniate, i.e. these sins cut the person off from the Church. But only when the sin is both formal heresy and to the extent of a mortal sin. The term ‘obstinate’ in the definition of formal heresy indicates that the choice is free and full, and that the knowledge of the sinfulness of the act is also full. So the type of heresy that automatically excommunicates is formal heresy to the extent of an actual mortal sin.
Many Catholics in the Church today are in a state of at least material heresy. And they do not seem to mind at all.
Generally speaking, Protestants are in a state of material heresy; Protestantism is a type of heresy. Many Protestants are in a state of formal heresy.
Orthodox Christians are in a state of formal schism. However, schism is often accompanied by heresy, and in fact Orthodox Christians generally reject, formally, a number of infallible teachings of the Magisterium.
Apostasy, heresy, and schism are particularly serious sins, because each inherently separates the Christian from the teachings of the Church, which are our guide to eternal life.
Not only is it a serious sin to commit apostasy, heresy, or schism, but it is also a serious sin to lead someone else into these sins. Many persons are guilty of using the internet, websites, and discussion groups, to commit the objective sin of attempting to lead people into apostasy, heresy, or schism (especially heresy).