Alot has happened in a day, and it looks like one Chris Smith (unknown to me, but I'll read more shortly as I catch up) has beaten me to the punch, but while I catch up let me post this outline of a position I was working on, which is suddenly rather topical.
CHRISTIAN: A name derived from that of Christ himself. The name refers to all those who have been anointed through the gift of the Holy Spirit in Baptism; hence, the followers of Christ, the members of the Christian Church. According to Acts 11:26 "it was in Antioch that the disciples were first called Christians" (1289). - Glossary of the Catholic Catechism
This post intends to illustrate the undesirability of conflating the terms "Christian" and "orthodox", emphasizing that we need both terms, one with a wide definition, the other with a narrow one, if we are to make any sense of history.
To begin with, as an appetizer, consider the natural-sounding expression "the Christians are debating orthodoxy again", or its historical equivalent "orthodoxy emerged from disputes in the Christian community". Neither expression is coherent if orthodoxy defines Christianity, for then orthodoxy cannot be debated among Christians; in any such debate, at most one side would be orthodox, and therefore at most one side could be Christian.
Historians of Christianity, of course, would like to say such things as "orthodoxy emerged from disputes in the Christian community", since that just makes sense. In order to do so, they need a broad sense of what Christianity is, so that both the "right" and the "wrong" (or winning and losing, or whatever) sides in a dispute about orthodoxy can be considered "Christian".
Thus, for instance, if I turn to my first (and still favorite) "A History of Christianity" by Kenneth Scott Latourette (American Baptist), in the preface I read:
Most of this will have to do with what we term Christianity. Christianity is a religion and as such is one of many religions. Its distinctive feature is that, as its name implies, it has Jesus Christ at its very heart. Yet Christianity is a synthesis of what the Christian regards as the Gospel, God's gift to man in Christ, and of the human response to it. Christianity centres about Christ, but it is compounded of the faith, Judaism, from which Jesus sprang and which prepared the way for him; of Jesus himself, his birth, life, teachings, deeds, death, and resurrection; of the faith of his immediate disciples in him; and of the several aspects of the many environments into which it has moved. Obviously, a well-rounded account of the history of Christianity will narrate the story of its geographic spread, taking account of the forms of the faith which spread... [and after another page of such generalities] If it is not to be distorted, the history of Christianity must include all the varieties of the faith. (xiv-xv)
Let's try to explore the bounds of this broad sense of Christianity with a test case, the Alexandrian priest Arius. If orthodoxy is defined in terms of, at least, the Nicene creed, and if the unorthodox are not Christians, then there should be no question of Arius' non-Christianity, since the Nicene creed was composed specifically to condemn him. But what is the story as reported by Latourette, i.e. as reported by a historian? The following is a severe abridgment of pages 151-164.
Two streams of thought emerged from the work of Origen, the conflict of which would result in the most serious division of Christianity to that time (4th century). One of the streams, today considered heretical, was championed early by Lucian of Antioch, who died in the persecution of 312, but whose work was carried on by his better known pupils, Arius of Alexandria and Eusebius of Nicomedia. I'll skip what the actual issues were (it's irrelevant to the question at hand). Arius and Eusebius were opposed by Alexander of Alexandria, Arius' bishop and immediate superior, and Athanasius (a deacon in Alexandria, later Alexander's successor as bishop). What could have remained a minor quarrel in a corner of the empire spread, in part because Arius composed a number of popular songs expressing his theology, which went viral (to use a modern term) and brought, for the first time in history, large masses of laypeople into what should have been an obscure theological quarrel. The Emperor Constantine called a council of all bishops in Christendom to resolve the dispute, in Nicaea, in 325 AD.
The council decided for Alexander and Athanasius, banished Arius, ordered the burning of his works, and published a creed (not our Nicene creed, but a first draft of sorts) that expressed the correct faith as determined by the council. After the council (at which Eusebius signed the creed), Eusebius was stripped of his see by the Emperor, and other supporters of Arius also lost their positions. Two years later, however, another gathering of bishops in the same city readmitted Arius to fellowship and reinstated Eusebius as a bishop, as it became immediately clear that while the council of 325 had been maneuvered into compliance, the Christian community at large was at least as suspicious of the apparently Sabellian [another heresy] doctrines of Alexander and Athanasius as it was of the doctrines of Arius and Eusebius. Besides, there was big politics involved: Arians dominated the eastern mediterranean, Nicaeans (as they came to be called) the west, Arians taught obedience to the Emperor, Nicaeans taught an independent sphere for the church (and within them, a growing splinter taught supremacy of the bishop of Rome). Within a year Eusebius was a principal advisor to the Emperor, and it would be the Arian confederate Eusebius who baptised the emperor shortly before his death ten years later.
Arius, though, died in 336, the year before Constantine's baptism. He was, at that time, a member in full standing of the church (since his return from exile years earlier), though he never received communion from the hands of Athanasius, his archenemy and bishop of Constantinople (the city on whose streets Arius suddenly collapsed). One legend has it that God struck Arius down miraculously to prevent his receiving communion from Athanasius, another has it that Arius was poisoned.
Anyway, the doctrinal position of Arius never changed; it was the church that zigged and zagged between the Scylla and Charybdis of Arianism and Sabellianism, until the Cappadocians formulated what would become the orthodox doctrine on this matter, some 40 years after Arius' death. At the time of his death, Arius' doctrine was in the ascendancy, so much so that at least one bishop of Rome (Liberius) is believed to have accepted Arianism, albeit under imperial threat of exile.
The rest of the story is a mess of compromise, with the Nicaeans shifting toward the semi-Arians, and the Cappadocians cutting the Gordian knot of reconciling anti-Sabellianism with anti-Arianism. The Nicene Creed as we know it today reflects this Cappadocian synthesis (and is drawn from a Jerusalem Creed which in turn was influenced by the first Nicene Creed), and is commonly associated with the council of Nicaea of 381, although it was not actually adopted there. Its origins are, however, roughly from the 380s, and its theology is similar to the Cappadocian synthesis adopted at Nicaea in 381.
So, today Arianism is named a heresy, as proclaimed in a Creed written long after Arius died, but apart from two years' banishment, Arius remained a member of the church all his life, albeit with continuing personal feuds with his ecclesiastical superiors, including denial of communion by his archenemy Athanasius. Latourette winds down the story thus (p. 164):
By a slow and often stormy process the overwhelming majority of Christians had come to believe that the formula which bore the Nicene name contained the correct statement of the Christian faith on the questions which had been at issue. Today most of those who are called Christians continue to honor it, along with the Apostle's Creed, as the official authoritative formulation of their faith and employ it in public worship.
Latourette clearly leaves room for non-Nicene Christians, both in the 4th/5th centuries and today. For the historian, orthodoxy is tighter than Christianity. I suggest that based on his lifelong personal faith and devotion to Christ and his church, Arius is one of those non-Nicene Christians.