I haven't read SPQR; I don't know what Mary Beard has to say about the Social War. From the reviews I've seen, and the interview of her I heard on I think Terry Gross's show I have the impression that the book is for the most part a fair exposition of the current orthodox (for lack of a better word) understanding of Roman history for non-specialists. Is that a fair evaluation? I'll work with that premise.

The general narrative of the Social War hasn't changed much since Mommsen in the mid 1800s. It relies heavily on the 2nd century CE historian Appian, since Appian is the earliest narrative account of the war to survive. It runs something like this: as Roman military commitments in the Mediterranean increased after Punic 2, Rome relied increasingly on her Italian allies to fulfil these commitments. Treaties that used to obligate Italians to provide soldiers for a few months a year, for the most part in and around Italy, became used to move troops abroad for decades. At the same time Rome used her allies to enact her foreign policy, she concentrated the benefits of that empire within Rome. Italians, seeing Rome take the benefits of the wars they were fighting, became increasingly demanding of access to Roman policy decisions through gaining the citizenship. Scipio Aemilianus, the general that destroyed Carthage in Punic 3, seems to have been one champion of Italian citizenship, this policy was continued by C. Gracchus (d. 121 BCE), and finally by the tribune of the Plebs Marcus Livius Drusus in 91 BCE. Drusus was assassinated in his home just before carrying his legislative project, including enfranchising the allies. Immediately on Drusus' assassination, citizens of the Italian city Asculum lynched the praetor Servilius, and a number of non-Latin allies revolted or threatened to revolt, and the peninsula very quickly fell into what one scholar called the greatest conflagration Italy has seen except perhaps the Hannibalic war (I think that's Keaveney?). There were significant losses on both sides, including the deaths of two consuls, and Rome was forced to concede the citizenship to first those allies who at least did not actively fight against Rome in 90 with the passage of the Lex Iulia de civitate, and the following year to rebels who surrendered with the Lex Plautia Papiria. Hostilities ended shortly, for the most part, although there were holdouts particularly among the Lucanians and the Samnites for about a decade until Sulla returned from his wars in Asia Minor, but these are footnotes. The major conflict was settled with the extension of the citizenship in 89. Keaveney said (I think I'm quoting this verbatim) "with the passage of this law [the Lex Plautia Papiria] the Italian question, which has been the subject of this book, had come to a close."

How long bitterness remained between Romans and Italians has been a point on which scholars quibble - Mommsen thought part of the Italian desire for citizenship arose from the emergence of an Italian nation-thingy (it couldn't be a true nation like our modern emerging German nation, because Italy never had a representative assembly [if that is the bar to nationhood, says LegalAction, you can't really talk about any nation until at least Women's Suffrage, so no, Mommsen, your German nation doesn't have that much on Italy]), so passage of the laws was enough to fix the problem. Syme, who thought all forms of government are really oligarchies, thought it took penetration of the Senate by a significant number of Italians under Caesar and Augustus. Keaveney, in his second edition, decided integration came not with the passage of the two laws, but with the first successful census of Italians - Rome tried to take a census in 86, but that was never completed. It took until 70 BCE to enroll Italians in across all the tribes in the voting assemblies. Before then, they were enrolled in only 10 tribes, limiting the impact they could have on the vote. Other people have put the end of that conflict at Sulla’s return from the East and his settlement of Italian affairs in his dictatorship (82 BCE)

If Mary Beard is telling this story, she’s about 20 years behind scholarship on the issue. Mouritsen published an influential if not universally well-received book in 1998 that tried to blow up this whole story, on the grounds that it relied too much on the evidence of Appian and on the nationalist worldview of Mommsen. Every point from the desire for Roman citizenship as a reason for the war to the connection of the citizenship leges with the end of the war has been challenged. Mouritsen worked backwards, sort of. By the time Appian was writing, the narrative of the Social War as a sort of civil rights movement had become the “traditional” story, and Appian fudged his dates to make them work with the narrative. Mouritsen despairs of the state of the evidence without Appian so much he actually claimed to be reconstructing his account of the war from the silence of the sources, which leaves people like Keaveney unimpressed to say the least. There isn’t really a new consensus yet, though more recent work tries to take Mouritsen’s criticisms seriously.

So how early can we find evidence of this “civil rights” narrative of the war? Claudius in his speech to the Senate in 48 CE spoke of the senate as the representative body of Italy (compared to the provinces). Velleius Paterculus fought with Tiberius in the early 1st century CE wrote that his grandfather (great-grandfather?) was an Italian commander that remained loyal to Rome in the Social War, and something like to exclude Italians from the citizenship was unjust, but it was a greater sin for the allies to wage war on Rome to correct that injustice. Augustus, of course, used Italia as a slogan in his war against Antony, or he claims to have in his Res Gestae, where he says he got a loyalty oath from “tota Italia,” but we’re not really sure what exactly what he means by “tota Italia,” “loyalty,” or “oath.” The historian and Caesar’s friend Gaius Asinius Pollio apparently was the descendent of a rebel general in the Social War and at least one interpretation of his snarky comment about Livy’s patavinitas “Padua-ism”? “Small-town-ness”?) is that he is at least not as un-Roman as Livy. Farney has an excellent book on ethnicity in Late Republican and early Principate Rome, and we find a lot of ethnic stereotypes deployed in the context of Roman political society, both positively and negatively. How much the deployment of stereotypes represents a schism between Romans and Italians? I don’t know yet.

There is also the question of whether ideology drives group formation, or if groups form and then ideology develops to justify the existence of the group. The “nationalist” or “Primordialist” (to borrow the term A. Smith uses) school would see things like the oath of Augustus as the result of a pan-Italian identity already having developed, while a “modernist” might see the oath as part of a developing ideology that then shapes the world to conform to it.

You asked your question at a time when we don’t have a very good answer, and you can see (I hope) a number of places someone might designate the end of the schism, depending on how they think of history, the sources, nationalism, and the state of the evidence.

Personally, I think the speech of Claudius in 48 CE is a hard terminus ante quem, and the conception of Italy as a territorial political state probably began to take hold under Augustus, though that idea extended to at least the Social War.