I think Flavius Josephus is generally regarded as a valuable historical source.
He has clear biases - he is trying to flatter the Romans and make himself look good - but historians rely on Josephus extensively and consider him reliable, especially when he says things that can be confirmed elsewhere.
On the passage you quote, I think most scholars would agree that some portion of it almost certainly goes back to Josephus. I suspect most would also say that it has been edited by later Christian scribes, but that's hard to prove. We do not have earlier versions of the text that are significantly different for that passage, so we can't use the text history to know if this is true. They are not saying that it is spurious, but that it probably did not say, for instance, that Jesus was the Messiah. They think it might have said something more like this:
About this time there was Jesus, a wise man. He performed surprising deeds and was a teacher of people who gladly accept the truth. He won over many Jews and also many Greeks. When Pilate, upon an accusation by the leading men among us, condemned him to the cross, those who had loved him from the beginning did not cease. And to this day the tribe of Christians named after him has not disappeared.
The main argument for this is that some of the early Fathers knew Josephus well, and did not think he believed Jesus was the Messiah. For instance, Origin says this:
https://en.wikisource.org/wiki/Ante-Nic ... Chapter_17
And to so great a reputation among the people for righteousness did this James rise, that Flavius Josephus, who wrote the “Antiquities of the Jews” in twenty books, when wishing to exhibit the cause why the people suffered so great misfortunes that even the temple was razed to the ground, said, that these things happened to them in accordance with the wrath of God in consequence of the things which they had dared to do against James the brother of Jesus who is called Christ. And the wonderful thing is, that, though he did not accept Jesus as Christ, he yet gave testimony that the righteousness of James was so great; and he says that the people thought that they had suffered these things because of James.
I hate that translation. Let me ask GPT to translate it more readably ...
James had such a strong reputation among the people for righteousness that Flavius Josephus—who wrote The Antiquities of the Jews in twenty books—when he tried to explain why the people suffered such terrible disasters, even to the point that the Temple was destroyed, said that these things happened to them as God’s judgment because of what they dared to do to James, the brother of Jesus who is called Christ.
And the remarkable thing is this: even though Josephus did not accept Jesus as the Christ, he still testified that James was extraordinarily righteous, and he says that the people themselves believed they suffered these calamities because of James.
1. Are we discussing the topic? Good.
2. Are we going around and around in a fight? Let's stop doing that.
3. Is there some serious wrongdoing or relational injury? Let's address that, probably not in public and certainly not for show.