I think Yohanan Hurkanos converted Idumeans, whoever they were at a time, then Alexander Yannai and his brothers before him relied more and more on Idumeans for military support. Alexander also conquered and converted Greek cities in Yehuda and and Transjordan. Note that we have kosher converts at that time, not all were fake (Shemaya, Avtalyon). Alexander made Antipater, Herod’s father, a governor. Antipater played an intermediate when Alexander’s sons, Aristobolus and Hyrcanus, invited Pompey to resolve their competing claims to malchut. Antipater was mostly in charge with Hyrcanus being nominally a king (source: Berel Wein’s book).
Does the fact that Rabbis criticized these conversions made them invalid? Were they treated as sofek as Samaritans? Anyone has sources for that? Bava Basra seems to treat him as ben eved, that would make him disqualified for malchut.