Have any of the old heresies (i.e. Manichean, Arian, Nestorian, Iconoclasm) been resurrected and repackaged by main-line denominations
-or-
Do Protestants, in general, still accept the pre-reformation doctrine which was formulated specifically to denounce such heresies? (i.e. Hypostatic union, Consubstantiation)?
...I'm pretty sure that heresies and doctrine I mentioned are widely denounced and accepted respectively among Protestants, so I'm not asking about those in particular.
By and large, Protestants follow Chalcedonian formulations in regards to Chalcedonian heresies.
Protestants by and large subscribe to hypostatic union, although our theories of communion vary widely from memorialism to consubstantiation. If you think in terms of the importance of these issues, however, the more "important" the doctrine (i.e. the nature of Christ is more important than the nature of the elements in the Eucharist), the more likely we are to agree.
Analogy to Common Law
The closest analogy would be like what happened in the Americas after we revolted from Great Britain. The UK had a long, established Common Law for crime, torts, etc... Those precedents in English Common law are still used in American Courts of Justice today. Why? Because it didn't matter if you had a President or a King - libel was still libel, theft was still theft, and double-parking was still rude. In the same way, old heresies are still heresies.
To stretch the analogy, however, what constitutes murder is almost identical. Libel, on the other hand, has far more nuance (and is much harder to prove) in the US than in the UK. Where does defamation become slander? Well, that's when you start getting lawyers involved.
If you ask any Christian outside of an obscure Dutch sect, "Is Jesus God?" You're going to get a yes. If you ask about Hypostatic Union, any priest or minister will agree. (And 90% of the people in the pew will say, um, sure, yeah.)
The point is, we agree on a lot.
What defines heresy?
Up until the rise of the Scholastic movement in the 1300s and the proto-reformers like John Wycliffe and Duns Scotus, there really was no such thing as a Protestant (or a Roman Catholic for that matter). There was simply "the Church." (I know someone's going to say "but what about the Orthodox?" They were part of "the Church" too, even if they were in disagreement about who was the head honcho.) Likewise, prior to 787 and the 7th Ecumenical Council, there was no Eastern and Western church - just the "church" (albeit with different Patriarchs). In regards to theological doctrine, there was (and still is) far more agreement than disagreement.
Look, for example, at the Nicene Creed. There is a heck of a lot of theology in that creed, and yet with the exception of one syllable at the end of filioque, 97% of the world's Christians can still agree on the entire summary! Each of the heresies noted by the Council of Chalcedon is a rejection of a tenet of that creed.
As such, most of the heresies as identified by the first seven ecumenical councils are regarded as heresies by modern Protestants as well. They are regarded as heresy by Orthodox and Roman Catholics too. There is a wide body of mainstream Christianity that really is a definable entity.
If someone tries to say that your salvation is dependent on a godly pastor, a Protestant can yell "Donatism!" as easily as a Catholic.
If someone says that Jesus was strictly God and not man, it doesn't matter if your RCC or Orthodox or Protestant, you can still say "that's Monophysite" and be right. (Incidently, a lot of Baptists are for all practical purposes Monophysite but don't know it.)
And to anyone who says that Jesus only appeared to be human or only appeared to die on a cross (like, say a Muslim), pretty much any Christian* can say "Docetism!"
Heresy simply means this - a theological position out of step with accepted majority thinking. Back in the days when people were persecuted for being out of step it meant something more, but nowadays, it just means whether or not the doctrine has historically been considered consensus or not. (Indeed, every heretic believed it was everybody else who was going to hell.)
How I learned to stop worrying and love the heresy bomb
To your original question of "What heresies are in the church today?" well, that's a book. The former dean of Virginia Theological Seminary once told me, "There are no new heresies, and there are no non-heretics. Everybody has a heresy, the question is simply which ones."
Trinitarianism and Christology are two classic examples of heresy breeding grounds. Between modalism and tritheism, monophysitism and monoergism and Nestorianism - there are so many errors on either side that the question isn't if one espouses a heresy, but which one. In practice, I'm sure I'm a heretic, but I at least can label my heresies :) The point is to note the error and seek to correct it in one own's theology (or point it out where there is a practical implication in others reasoning) rather than worry about or ignore it.
*Now - does that mean that there are some people who claim to Christian but hold to heresy?
Yup. Doctrinally speaking, Christians are not pure. We hold all sorts of mysteries in tension, and as such hold to heresy from time to time. By the measurement of Chalcedon, some groups are further away than others. It isn't a opinion, its a demonstrable fact. Historically, that's been the most widely accepted definition of Christianity ever.
Does that mean Chalcedon was 100% correct? That's when you start getting into bar-room philosophy and theological brawls. But if you just want to know what the (mainstream) Christian world calls heresy and what it doesn't, that's the place to start.
Yes there are a few, at least.
I used this list of heresies. However, it seems that some aren't extremely old. Tritheism, for example seems to have originated in the 10th century.
After the Reformation, Arianism began popping back up. Jehovah's Witnesses even practice a form of it. (Although the disagree with Arius' views in many respects, they follow the idea that Jesus was a created being.) Also, the Church of God (7th Day) believes in Arianism.
Donatism also seems to have somewhat of a resurgance with Anabaptists or Confessional Lutherans.
It seems that Kenosis may be accepted by some (no idea which denominations, though).
Theosophy was preached as recently as the early 20th century. It should be noted that it was a Catholic bishop (for the Liberal Catholic Church) who preached this doctrine though.
It's also been argued that Pelagianism is being taught in the Mormon church.
Subordinationism is alive and well in many denominations.
Finally, Tritheism seems to be present in the Seventh-Day Adventist denomination.
Edit to modify for the moving target.
Unfortunately, each heresy is a big topic on its own. Arguing for or against Tritheism, for example, (or Arianism, or Subordinationism, etc.) would lead to huge answer and a debate topic.
As it is, some people believe in some of these heresies, some do not. Debating each side of each heresy would be beyond the scope of a single answer.
According to the first chapter of the Westminster Confession:
VI. The whole counsel of God, concerning all things necessary for his own glory, man's salvation, faith, and life, is either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture: unto which nothing at any time is to be added, whether by new revelations of the Spirit, or traditions of men. Nevertheless we acknowledge the inward illumination of the Spirit of God to be necessary for the saving understanding of such things as are revealed in the Word; and that there are some circumstances concerning the worship of God, and government of the Church, common to human actions and societies, which are to be ordered by the light of nature and Christian prudence, according to the general rules of the Word, which are always to be observed.
For Protestants, the first line of defense is the Scripture. This comes from Paul himself:
2 Timothy 3:16-17 (ESV)
16 All Scripture is breathed out by God and profitable for teaching, for reproof, for correction, and for training in righteousness, 17 that the man of God may be complete, equipped for every good work.
The Confession makes specific allowances for the role of the Spirit in the interpretation of Scripture—in particular when it comes to doctrines of salvation. Of course, Scripture doesn't cover everything: specifically "the worship of God, and government of the Church". Therefore, we are encouraged to use "the light of nature and Christian prudence" to order them. I think that means reason and common sense.
Finally, we confess that we should always observe the general rule of the Word. To me, that means to double-check our beliefs against Scripture. This is the essence of what we mean by Sola Scriptura.
So that's the backdrop. Let's see how we might apply that to a topic that's been on my mind lately: Iconoclasm. Should we have images of saints or Christ or anything else in our places of worship?
First cut: Exodus 20:4 commands us not too make carved images of anything for the sake of worship. Therefore, no images in church.
Second cut: Over the years, the church has allowed images. In fact the second Council of Nicea ruled that images are allowed because of the Incarnation. Perhaps the simple reading of Exodus is mistaken.
Third cut: Relying on the Holy Spirit for wisdom in interpreting the Bible, we go back to relevant New and Old Testament passages and try to understand if the arguments made by Christians in the past justifying images hold water.
The informal motto of the denomination I was confirmed in was "Where is it written?" What that means is that we are always going back to the bedrock of our faith, the Bible, to answer questions of faith. History and tradition have their place, but the Reformation remains committed to weeding out anything that hinders our relationship with God and holding tight to what God's Word affirms.
