Adultery, by Republican law, was probably not prosecuted as a single offense. The Augustan lex Julia de adulteriis coercendis established adulterium as a criminal offense (as opposed to the civil offense it had probably been earlier) and carried harsh penalties extending even to the loss of conubium. The lex Julia established a clear distinction between adulterium, illicit sexual relations between a married woman and a man other than her husband, and stuprum, similar sexual relations between (free, of course) unmarried women and men, which might include rape. But Republican law had no clear distinction, and punishment of adultery was largely an individual affair. The precise procedure and penalty for such actions is quite unclear before the establishment under Augustus of regular court proceedings against adulterers. Action against the wife was frequently taken privately, by the pater familias, and usually included divorce and possibly even execution. Republican stuprum probably justified actions of deliberate murder of both adulterers and adulteresses, and probably adulterium did as well (c.f. Solon's law at Athens that established the right of a husband to kill an adulterer without court proceedings, while also noting that Athenian law basically ignored the woman's existence in adultery proceedings). By Cicero's time at least adultery, both stuprum and probably adulterium, had mainly moved into the realm of civil iniuria, that is lawsuits for damages. Under Augustus stuprum was divided into willful, unwillful (i.e. without knowing the status of the woman), and attempted. Of the three only willful stuprum was considered a criminal offense (to which crimen vis, the crime of violence, might be added if rape was involved); the other two forms were only civil cases of iniuria. Before Augustus it's unlikely that this distinction existed, and the relatively free prosecution of adultery as adulterium, stuprum, and simply general iniuria left a great deal open to interpretation. What is clear is that the letter of the Republican law granted the injured party quite a lot of leeway in retribution and establishing their own private justice (Roman law, after all, recognized iudicium domesticum, "household court," or the right of the pater familias to manage the affairs of his own household).

Publius Clodius was not prosecuted under any of these laws. Publius Clodius infiltrated a celebration to the Bona Dea, overseen by the Vestals, supposedly with the intention of committing adultery (this latter was, even in antiquity, not really believed, and most scholars disregard it for various reasons relating to the timing of the charge). Publius Clodius' offense was the violation by his very presence of a Vestal rite, endangering pax deorum, a serious criminal action. But pax deorum had not been violated, since the Vestals redid the rite the next day. The avenue to prosecute Clodius on religious crime was closed as quickly as it had opened, and those interested in prosecuting the tribune-to-be had to search around for other possibilities. Caesar's divorce of Pompeia came after Clodius was dragged into court, not before it, and as Clodius' enemies searched for a means to prosecute him Caesar simply did nothing, only afterward going with the general flow. Caesar probably would have prosecuted Clodius either under stuprum (though there was no evidence that any action had taken place, and even a charge on attempted adultery was shaky) or possibly simply as iniuria, which apart from the iniuria of possible unlawful relations within his household (a slavegirl was also implicated later) also could include damages done to one's dignitas, though it was dicey legal territory. That there was a complicated legal struggle over whether even to prosecute Clodius at all is clear enough from Cicero's letters, and Murena, the consul presiding in December of 62, as well as Pupius Piso, the new consul presiding in January of 61, were Clodius' friends and ignored the Bona Dea question. Roman law in the Republic only accepted two strict forms of religious delict in cases when the pax deorum remained intact, sacrilegium and incestum. The former applied to stealing ritual implements and was clearly not applicable, and the latter applied either to actual incest or, more usually, to the charge against a Vestal of breaking her vow of chastity. Cornificius, a praetorian who had failed in a consular bid against Cicero in 64, at last presented the motion to prosecute Clodius after pretty much everybody in the senate had decided to let it go, by which action the senate was forced to refer by senatus consultum to the priestly colleges who, their opinion finally being solicited, promptly declared Clodius' actions nefas. A court was set up to try Clodius with incestum, the nearest thing that Clodius could reasonably be prosecuted for. Cicero's accusations of Clodius' actual adulterous incest with Clodia only appeared during court proceedings, so they had nothing to do with the actual charge brought against him, and there was no evidence that any Vestals had broken their vows. Clodius was prosecuted by proposing a special (I would argue illegal) bill that expanded incestum to include specifically the violation of the Bona Dea, and no other Vestal rites. The prosecution of Clodius is rather odd for a number of reasons, but had Caesar pressed charges they would not have really been about adultery--rather, Clodius' supposed adultery would have been an excuse. Whether we imagine that Caesar did nothing as a beneficium to Clodius, because he saw no evidence of its occurring, or to protect his own dignitas from the disgrace of a public proceeding on adultery does not particularly matter. Nor was Caesar's action especially unusual. Such official inaction in matters of adultery were not especially uncommon in the Republic, as Republican law placed a great deal of the responsibility for action against adultery on the offended party and had poor official channels by which to pursue such action.