Religion

Well, that's pretty easy, but discussing the person and the reasons to be skeptical because of their past behavior is still quite relevant. And you have two links in the past comment on that point.

As for the article's points, let's take a look at just one that Carrier puts forward, that the bit about James brother of Jesus was about the high priest.

Look closer at Josephus:

Festus was now dead, and Albinus was but upon the road; so he assembled the sanhedrim of judges, and brought before them the brother of Jesus, who was called Christ, whose name was James, and some others, [or, some of his companions]; and when he had formed an accusation against them as breakers of the law, he delivered them to be stoned: but as for those who seemed the most equitable of the citizens, and such as were the most uneasy at the breach of the laws, they disliked what was done; they also sent to the king [Agrippa], desiring him to send to Ananus that he should act so no more, for that what he had already done was not to be justified; nay, some of them went also to meet Albinus, as he was upon his journey from Alexandria, and informed him that it was not lawful for Ananus to assemble a sanhedrim without his consent. 2 Whereupon Albinus complied with what they said, and wrote in anger to Ananus, and threatened that he would bring him to punishment for what he had done; on which king Agrippa took the high priesthood from him, when he had ruled but three months, and made Jesus, the son of Damneus, high priest.

• Josephus Antiquities book 20

See how Josephus introduces a Jesus twice?

The problem with Carrier's theory is that Josephus doesn't once introduce someone's father after mentioning them before (with one small exception that actually makes the case here even worse). So even if the 'called Christ' was added in later on, mentioning an ambiguous 'Jesus' before identifying the one that's the high priest would be the only time someone is introduced in the text after being mentioned. Or else it would be the only time two people by the same name aren't distinguished from each other.

A number of months back I actually tried to argue Carrier's point on this issue with one of his critics, and in the course of that went over every single introduction in all of Antiquities trying to find another exception.

There aren't any.

Carrier's case here isn't strong at all and necessitates this mention being the only one of all the introductions that breaks Josephus's convention.