The Qumranites included priests, "Sons of Zadok" among their number, if the Community Rule (1QS) is an accurate reflection of actual practice.
I think that they expected that their philosophy would eventually rule in the Temple. The War Scroll (1QM) describes "years of remission" when the war against the "Sons of Darkness" ...
From Rashi there:
כל איש אשר בו מום. לְרַבּוֹת שְׁאָר מוּמִין:
NO MAN THAT HATH A BLEMISH… [SHALL COME NEAR] — This is intended to include in the prohibition (besides the blemishes expressly mentioned in vv. 18—20) also other bodily blemishes (Sifra, Emor, Chapter 3 1).
מום בו. בְּעוֹד מוּמוֹ בּוֹ פָּסוּל, הָא אִם עָבַר מוּמוֹ כָּשֵׁר (ספרא):
HE HATH A ...
The following website writes as follows:
Although the Beta Israel — the Ethiopian Jews, a minority of today’s Israeli population, who mostly came to the country in two waves in the 1980s and early 1990s—maintain the priesthood tradition, they are unique in that they do not consider it to be hereditary. Instead, the Beta Israel priest, called as Kes or Kahin ...