Here is how Josephus introduces Judas the Galilean in Book 17 of the Antiquities:
There was also Judas, (16) the son of that Ezekias who had been head of the robbers; which Ezekias was a very strong man, and had with great dificulty been caught by Herod. This Judas, having gotten together a multitude of men of a profligate character about Sepphoris in Galilee, made an assault upon the palace [there,] and seized upon all the weapons that were laid up in it, and with them armed every one of those that were with him, and carried away what money was left there; and he became terrible to all men, by tearing and rending those that came near him; and all this in order to raise himself, and out of an ambitious desire of the royal dignity; and he hoped to obtain that as the reward not of his virtuous skill in war, but of his extravagance in doing injuries.
Whiston's footnote:
Unless this Judas, the son of Ezekias, be the same with that Theudas, mentioned Acts 5:36, Josephus must have omitted him; for that other Thoualas, whom he afterward mentions, under Fadus the Roman governor, B. XX. ch. 5. sect. 1, is much too late to correspond to him that is mentioned in the Acts. The names Theudas, Thaddeus, and Judas differ but little. See Archbishop Usher's Annals at A.M. 4001. However, since Josephus does not pretend to reckon up the heads of all those ten thousand disorders in Judea, which he tells us were then abroad, see sect. 4 and 8, the Theudas of the Acts might be at the head of one of those seditions, though not particularly named by him. Thus he informs us here, sect. 6, and Of the War, B. II. ch. 4. Sect. 2, that certain of the seditious came and burnt the royal palace at Amsthus, or Betharamphta, upon the river Jordan. Perhaps their leader, who is not named by Josephus, might be this Theudas.
Loeb's footnote is that this character appears to be the Judas the Galilean who created the fourth religious group in Palestine in that era.
However, the traits and descriptions that I put in bold above seem very different than what one would associate with the Christians' qualities. The Christians did not seem to be an anti-Roman rebel group killing each other and stealing sums of money to declare someone named "Judas" a ruler.
So:
Is this the Judas who supposedly created the fourth religious caste of Palestine in the 1st century?
Is that religious caste related to the Christians?
Is this the same group that Epictetus had in mind?
What is one to make of the numerous times that "Christians" are also called not just Nazarenes, but also given the title of Galileans in the sense of a sect by that name?
One possible answer: The "Galileans" were in fact a religious movement of whom Judas the Galilean, as well as Jesus and the Christians, were each different leaders and components. Maybe the Christians were a subset of the religious movement called Galileans?