What political faction? There's no political faction. Seneca's dabble in vegetarianism (it appears to have only lasted a year, or a little longer) is referred to in Epistle 108. Seneca adopted vegetarianism during his time with the Pythagorean Sotion. Seneca says that Sotion actually encouraged his skepticism in Pythagoreanism and nurtured Seneca's later well known maintenance of his own independent thought by telling Seneca that if he later came to believe the same as the Pythagoreans he'd be doing right, and if he continued to think his own thoughts he would be practicing Stoic frugality. The young Seneca couldn't go wrong by giving up meat.

But of his abandoning of Pythagorean vegetarianism Seneca says this:

Alienigena tum sacra movebantur, sed inter argumenta superstitionis ponebatur quorundam animalium abstinentia

The foreign cults were then being expelled, and among the indications of their belief was considered abstinence from certain kinds of animals.

The text is apparently corrupt here, though only in word forms: its meaning is obvious. This is using Gummere's text, since I don't have the OCT on hand. Gummere's translation for the Loeb is strange, since it translates movebantur as "inaugurated," which is possible, but in context certainly wrong. Seneca must mean either "expelled" or "disrupted." Gummere's own note seems to suggest that he's aware it's wrong, because he notes that the passage must be referring to the same incident as recorded by Tacitus at Ann., 2.85:

actum et de sacris Aegyptiis Iudaicisque pellendis factumque patrum consultum ut quattuor milia libertini generis ea superstitione infecta quis idonea aetas in insulam Sardiniam veherentur, coercendis illic latrociniis

And it was resolved against the Egyptian and Jewish cults and a senatus consultum made that four thousand of freedman rank infected by that belief who were of suitable age [that is, for military service--conscription never ceased in the Roman military, though it passed out of Italy, and freedmen especially were frequently conscripted in the early Principate] should be taken to Sardinia, to subdue bandits there.

Seneca tells us this happened during the reign of Tiberius, in his own youth--this is almost certainly the incident to which Seneca is referring (hence movebantur). So even though if you Google it you'll get a lot of garbage about Seneca giving up vegetarianism to avoid being prosecuted by Nero for being a Christian or Christian sympathizer, these are not Christians and this is not Nero. Seneca outright tells us this was under Tiberius (In primum Tiberii Caesaris principatum iuventae tempus inciderat). Josephus refers to this same incident at A.J. 18.3.4‑5. Josephus notes two scandals. In the first place, the priests of the temple of Isis were bribed to trick Paulina, a Roman initiate of the cult, into committing adultery. In the second, Josephus claims that a group of four Jewish exiles conspired to defraud Fulvia, a Roman convert, to give money to the temple, which they stole for their own purposes. Josephus distinguishes between two punishments. Tiberius destroyed the temple of Isis, and crucified those responsible. Likewise, Tiberius expelled the Jews from the city, and sent four thousand of them to Sardinia as soldiers--it is to this that Tacitus is referring.

There's no political faction, and I'm confused where it's coming from. Seneca--or, more accurately, Seneca's father, though Seneca denies this emphatically--feared legal action on account of a perceived similarity between his Pythagorean diet and the dietary restrictions of the Jews and apparently of initiates into the cult of Isis. These cults were not "political factions," but had incurred imperial ire for their part in scandals targeting Roman citizens, which Tiberius did not accept.