Helen Bond summarizes the usual scholarly view.
The conventional view is that the Zadokites held the high priesthood only until the disturbances in the second century B.C.E. that led to the Maccabean revolt. The high priesthood was then claimed by the heirs of the Maccabees, the (non-Zadokite) Hasmoneans, who held the position until the reign of Herod I. Later high priests are generally regarded as insignificant, non-Zadokite priests, plucked from obscurity by Herod or the Roman governors and installed as puppet high priests, with no personal claim to any kind of authority in the eyes of the people. (Caiaphas, pp. 149-50).Bond goes on to say: "There is, however, very little evidence for this view" (p. 150), by which she refers specifically to the latter part of her summary, about the priests chosen by Herod. She suggests that these may well have been Zadokite priests. Bond repeatedly refers to the Hasmoneans themselves as non-Zadokite.
But were the Hasmoneans non-Zadokite? Nearly a decade ago, Alison Schofield and James VanderKam published an article in JBL questioning the scholarly consensus. You can read how they analyze the data for yourself, but here's their conclusion: “we have considerable reason to believe that the Hasmoneans were a Zadokite family and no evidence to the contrary” (87). Some others also cast suspicion on the usual scholarly view, e.g., Joshua Efron (p. 58 n. 55), Alice Hunt (who doubts the existence of Zadokites, but note this review by Deborah Rooke), and Regev Eyal (pp. 120-24).
On the other hand, Hanan Eshel goes the other way:
As opposed to Alison Schofield and James VanderKam, it seems that since we do not find explicit statement [sic] saying that the Hasmoneans were Zadokites, we should assume that they were not from this family. Schofield and VanderKam believe that since we do not find an explicit accusation saying that the Hasmoneans were not from the House of Zadok, we must assume that they were. (55 n. 71; see also p. 60; but Collins [p. 97 n. 43] charges Eshel with mis-representing the argument of Schofield and VanderKam)Timothy Wardle argues in the same way as Eshel, and considers the last line of Schofield and VanderKam's article (quoted above) to be "much stronger than the evidence suggests" (p. 73 n. 90).
I can't solve this problem, though I think Schofield and VanderKam especially have demonstrated that there is at least enough doubt to warrant some reservation in declaring the Hasmoneans as non-Zadokite. I'll have to revise some of my lecture notes. I'll also need to have a look at Deborah Rooke, Zadok's Heirs, which I haven't been able to do yet.
I'd like to know where the idea came from that the Hasmoneans were not Zadokite. I believe it is assumed already by the original Schürer (2.2.41). It appears that Wellhausen considers the possibility that the Hasmoneans are non-Zadokite, but he is not sold on it (Pharisees and Sadducees, pp. 76, 81, 82). He cites Geiger (1810-1874) as affirming it. And here's a note from Albert Baumgarten:
The notion that the rise of the Hasmoneans created a fundamental change in Jewish life, with the attendant demotion of the old Zadokite families, is an old one. It goes back, in one form or another, at least as far as A. Geiger [...].Baumgarten cites Geiger's Urschrift und Übersetzungen der Bibel (orig. 1857), pp. 101-2; and his Judaism and Its History (orig. 1866), pp. 102-3.
Apparently since Geiger's time (or before?) the tendency to classify the Hasmoneans as non-Zadokite (whether rightly or wrongly, I'm not at this point sure) has been so strong that even VanderKam seems to assume it in some of his other publications, such as The Dead Sea Scrolls Today (19941, p. 101 = 20102, p. 129; also Meaning of the Dead Sea Scrolls, p. 286; but not From Joshua to Caiaphas, p. 270 n. 90).
For sane summations of the data and scholarly opinion, it's hard to do better than John Collins.
The Hasmoneans were not Oniads; they did not belong to the family that had occupied the office in the third century BCE. But they may still have been Zadokite by genealogy. Conversely, it has been noted that "Zadokite" was by no means a standard or common way of referring to the high priestly line in the Second Temple Period [here citing Hunt's monograph, noted earlier]. The appeal to "sons of Zadok" in the Scrolls is primarily a claim of spiritual superiority rather than genealogical legitimacy. (pp. 97-98)As Collins goes on to note, this has major implications for how the origins of the Qumran community is envisaged, and, whether Schofield and VanderKam have succeeded in their case for a Zadokite lineage for the Hasmoneans, they have at least succeeded in demonstrating that there is not much ancient discussion of Hasmonean lineage in our ancient sources, suggesting that it was not such a big deal to them as it has been in modern scholarly imaginations.
UPDATE (3 Jan. 2014): just got notice from Jack Sasson of the publication by Vasile Babota of his dissertation, The Institution of the Hasmonean High Priesthood (Brill). From the Google Books preview I can't quite tell how he answers our question (or to what extent he deals with it), but it looks like (from pp. 274ff.) that he says that it was more important for priests to claim descent from Aaron than descent from Zadok in the second century BCE.