I have vague familiarity with Litwa, and per a not bad question about him and actually good response on this post at r/AcademicBiblical, I have some thoughts on Alan Kirk's review of Litwa's "How the Gospels Became History."
I do NOT think Kirk has the better of Litwa, but that's not the only thing involved.
First, my familiarity with Litwa is not so much directly with him, but with the "bios" school of New Testament, and specifically, gospels, exegesis. As No-Moremon notes in his response, this includes Robyn Faith Walsh and others.
First, contra Kirk, the "bios" idea can be used as a scaffolding around which to construct social memory ideas. That, of course, from my point of view, though, means the scaffolding came first.
Second, on the idea that this discounts conflict between Judaism and Hellenism? While Kirk may be right that at times, Litwa strains on finding specific Hellenistic parallels rather than mining the Hebrew Bible, Kirk in turn oversells this. Mark portrays a Jesus in conflict with "Herodians" and "Pharisees" and "Sadducees," but not, contra Matthew's Passion-crowd bloodlust, let alone John's "The Jews," is Jesus shown in conflict with the Jews in general.
So this?
“Hellenistic,” however, describes not so much a cultural homogenization as the fraught cultural encounter of rich national traditions with Greek culture, on a spectrum of assimilation, adaptation, and resistance.
Not so totally so, especially if Kirk thinks Litwa is describing homogenization.
Besides, per Lee Levine's great "Judaism and Hellenism in Antiquity: Conflict or Confluence?", the idea that Judaism wouldn't incorporate Hellenistic mythos is simply not true.
Beyond that, as early as Justin Martyr, Christian leaders acknowledged that the tales about Jesus' virgin birth were like those in the Greek world — only true. Otherwise, Adam Gopnik notes that Elaine Pagels' new book compares early Christians' evolving views about Jesus' post-death to Lubavichers' about Rebbe Menachem Schneerson. Gopnik notes that believe in a Lubavicher Moshiach redivivus would have surged had anything like the Jewish Revolt hit the Lubavicher community.
But? This is NOT a nod toward Litwa's "bios." Rather, it's Pagels' way of explaining how "rips" in the fabric of memory were restitched. Indeed, from there, Gopnik first pivots to Richard C. Miller, with whom I am unfamiliar, and then Walsh.
And so, why wouldn't the Gospelers use, and adapt, specific bits of Greek legend and myth? There, Pagels at least gets the overhead right. As for any Eastern myth Litwa might say backs the gospels, well, Levine notes that Judaism had been extensively Persianized before this. Emphasis on extensively, in my eyes. Idan Dershowitz, per what he says was originally The Great Famine, not Flood, has tackled this issue in detail.
Third, that said, is Litwa really that new? To riff on D.F. Straus, mentioned by Kirk, is this really that much different than a repackaged θεῖος ἀνήρ theory with a broader background?
And, per personages like Metatron in some of the Jewish apocalyptic literature from Qumran, that idea was not totally alien to Judaism before the gospels, either. Nor, however its theological interpretation is skinned, was the מַלְאַךְ יְהוָה or "angel of the Lord." And, Kirk knows this as well.
The search for the historical Jesus
Fourth, but not spoken in detail, I think is Kirk's real plaint. And that's that, as noted, Litwa is shutting the door on new searches for the historical Jesus.
And, really, it should be shut.
On the gospels, stand or die on Markan priority or not, whether you're pushing the communal social memory idea of the gospels' writing or not. As I see it, this is in some ways, with the Synoptics, an attempt to work around, or dodge, traditional theories of transmission, as was the push for oral transmission in the 1970s-90s, riffing off the Balkan bards of Parry and Lord. And, in part because social memory can be just as malleable as individual memory, I see it as being not much more likely than oral transmission theory to say anything significantly new about composition of any of the canonical gospels, let along the Synoptics. Oh, and yes, social memory can be that malleable; it starts with the sociology of crowds.
Perhaps Litwa could use more of the traditional 20th-century exegetical forms and methods. Perhaps use new ones, like the social memory idea, without over-leaning on it.
But, accept that you'll never get back further than an author's, or an author and his community's, ideas about the historic Jesus.
Period.
That's for you, and others of like mind, Alan Kirk.
To riff on Bultmann? The Christ of faith is all you can find.