Well, when it comes to “the early church”. it’s not exactly an even playing field.
Iconoclasm v. Iconodulism for example…for a long time the former was the majority position while the latter was fighting for its life. At other times Arianism or some species of Modalism seemed to be gaining the upper hand (thus “Athanasius Contra Mundum”).
Eventually, both Iconodulism and Trinitarianism won out but their having done so doesn’t necessarily mean that they are right, just that they are “orthodox”.
Now, I happen to accept the Trinitarian view but mainly because it is the only way that God as He reveals Himself in Scripture “makes sense” if that makes sense. I am gratified that the church has, historically agreed with me.
As for iconoclasm, I have no problem with images of Christ and so on, I have some difficulty with their uses in worship but it’s not a major issue except that I am sometimes bothered by the mental gymnastics we have to undergo to justify them; e.g. “We’re not worshiping the image, we are “reverencing” what the image represents” or “We consider the icon ti be a window into the life of God, through which we see Him and He blesses us” etc.) Similar things may be said by pagans of their idols. The better educated ancient Greeks didn’t worship statues anymore than Catholics do today…
Anyhow, No Protestant church espouses Nestorianism though a great many have trouble with the idea of the Theotokos.
Many Reformed are practical iconoclasts, purely speaking, but again, I don’t think Iconoclasm is heresy.
Many Evangelicals are practical Pelagians, but then, many Catholics are as well. No Protestant church officially endorses the view however.
Jansenism in its milder forms ought not to have been condemned as heresy by the church. It can be argued that Jansenism is the single most important social reason that Calvinism did not overtake the French church. At any rate, at it’s heart it’s just Augustinianism fully, though occasionally unskillfully, realized. It’s condemnation probably had more to do with the French monarchy’s ideas of divine right and the church’s terror of Calvin.
Anyway, I don’t know that any Protestant churches espouse it though many do espouse the Febronianism that descended ideologically from it, at least, again, practically and inasmuch as it represents a sort of Erastianism.