If that is true, then was there a valid high priest at all during the times of Our Lord?
Depends on what you mean by ‘valid’. After the exile, the priestly line which held the office for most of the Persian and Hellenistic periods traced their ancestry to Zadok. By the time of the Maccabean revolt against the Seleucids,
Jonathan ‘Apphus’ Maccabee (who were priests, but not of the Zadokite line) took the high priestly office, initiating the
Hasmonean line. Soon the Hasmonean high priests also began to wield political authority over the now-independent Judea, taking the title of
basileus ‘king’. This dynasty of priest-kings would continue until Herod the Great had
Antigonus executed in 37 BC. Herod first had a guy named
Hanameel (who, while being a priest, was neither a Hasmonean nor a Zadokite) become high priest after Antigonus, then decided to put the Hasmonean
Aristobulus III into the office (he was related to Herod by marriage, Herod’s wife Mariamne being his sister), only to change his mind soon and reinstate Hanameel afterwards. It was then that Herod (and soon, the Roman prefects and procurators) apparently decided to just appoint people into the position.
If you’re wondering where the Zadokites went after all this:
Onias IV, son of
Onias III, was originally the lawful heir to the office, but the elder Onias’ brother
Jason eventually became the high priest in 175 BC with some help from Antiochus Epiphanes. He apparently expected Judah Maccabee’s revolt to aid him in getting the office he was supposed to inherit in the first place, but seeing as things did not go as he expected them to be, he went down to Egypt to seek aid against the Seleucids at their political enemies, the Ptolemies. Onias and the other Jews who travelled with him settled down at
Leontopolis and built
a temple of their own there. Apparently Onias thought that the temple in Jerusalem had been totally defiled and hoped that the new one he founded would be a fitting replacement for it, but the folks back in Palestine apparently did not accept his claims and considered it an illicit act.
So, if by ‘valid’ you mean ‘Zadokite’, you could say that the Jews in Palestine did not have a ‘valid’ high priest for more or less a couple of centuries by then. Not to mention that the Maccabees are to blame for instituting a new line which overthrew the Zadokites out of office.
P.S. The hereditary Zadokite line in Judea pretty much ended with Jason. His two successors,
Menelaus (c. 172/1-162/1 BC) and Alcimus (162/1-159 BC) were not related to the family. (Josephus says that Menelaus was Jason’s and the elder Onias’ brother, although 2 Maccabees 4:23 says that he is the brother of a different Simon, the one who denounced the elder Onias to Antiochus.) In fact, Menelaus and Jason had a bit of serious rivalry about who gets to be high priest.