The Catholic Study Bible says the following about the Hasmoneans, the priesthood that took over in Jerusalem after the Jews' defeat of Antiochus Epiphanes (second century B.C.E.):
"The purpose of 1 Maccabees is clear: it defends the legitimacy of the Hasmonean dynasty...[T]he Hasmoneans functioned as high priests even though they were not descendants of Aaron as required by tradition. The principal opponents of the Hasmoneans were the Hasidim (the Pious Ones) who were the spiritual ancestors of the Essenes and the Pharisees. The Hasidim saw themselves as careful observers of the law but held the Hasmoneans to be illegitimate interlopers as religious and political leaders. 1 Maccabees tries to show that the Hasmonean dynasty owed its origins to a revolutionary movement that had zeal for the Torah at its heart. The Hasidim, on the other hand, were not always very prudent in their self-styled devotion to the Torah. In their concern to have a high priest from the family of Aaron, they acquired a collaborator who betrayed them (7, 8-18)" (RG 225).
I may be misreading this, but the Catholic Study Bible seems to be denying that the Hasmoneans were from the house of Aaron. It says that the Hasidism wanted a priest who was from Aaron's family, and that they disliked the Hasmoneans. That must mean the Hasmoneans weren't from Aaron's family, right?
But I Maccabees claims that they were. I Maccabees 2:1 says that Mattathias (father of Judah the Maccabee) was a "priest of the family of Joarib." And I Chronicles lists Jehoiarib as a descendant of Aaron (9:10; 24:7).
The Catholic Study Bible may be basing its argument on I Maccabees 7:8-18, in which the Hasidim embrace Alcimus because he's a priest of the house of Aaron. "A priest of the line of Aaron has come with the army, and he will not harm us," they exult, right before Alcimus proceeds to kill them. Was I Maccabees arguing against Aaronide descent being a criterion for priesthood?
Not necessarily. The Hasidim may have been excited to get an Aaronide high priest, for the simple reason that Alcimus' predecessor, Menelaus, was not one. Menelaus was the brother of Simon, who was of the house of Benjamin (II Maccabees 3:4; 4:23).
But not everyone agrees with that notion. In the HarperCollins Study Bible, Daniel Harrington states regarding II Maccabees 3:4: "Simon was more likely from the priestly clan of Bilgah (Neh 12:5, 18; 1 Chr 24.14), not of the tribe of Benjamin." Harrington doesn't support this statement, but he may be assuming that the Jews wouldn't tolerate a non-Aaronide high priest, so Menelaus had to be from a priestly family to get off the ground.
Personally, I think that the Hasidim in I Maccabees 7 were just gullible about the house of Aaron. I don't think I Maccabees in that scene is ruling out the criterion of Aaronide descent for the high priesthood.
Still, there was concern about lineage. The Maccabees were indeed descendants of the family of Aaron, but not through Zadok. The Zadokites were the high priests before the Hasmoneans took over, and they most likely resented the Maccabees taking their position. The Dead Sea Scrolls refer to the Zadokites on numerous occasions (e.g., Zadokite Fragments, Community Rule 5, etc.), indicating that the Qumran community had some pretty upset Zadokites. And they could appeal to the Bible to support their claim to the priesthood, for Ezekiel 44:15 states: "But the levitical priests, the descendants of Zadok, who kept the charge of my sanctuary when the people of Israel went astray from me, shall come near to me to minister to me; and they shall attend me to offer me the fat and the blood, says the Lord GOD" (NRSV).