Public violence was not treated cavalierly at all in the Roman world, and you're somewhat misunderstanding the two incidents to which you refer. The murder of Caesar is clear-cut: the city was thrown into complete confusion. People rushed around looking for safety, the conspirators marched through the streets with drawn weapons and barricaded themselves in the Capitol, and Lepidus marched his troops into the city. Though Antony seemed to have worked out a diplomatic settlement that temporarily settled the threat of civil war, in reality the city's instability threw it within weeks back into a state of utter chaos, resulting not long thereafter in the flight of the conspirators and the beginnings of preparations for civil war. The murder of Antyllius (or Antyllus as Appian calls him) by partisans of Gaius Gracchus is described by Plutarch as causing among the πλῆθος (the crowd) that they became διεταράχθη, which your translation translates amusingly as "consternation"--it means confused, disordered, or panicked. It's quite a strong word. Appian, who seems to think that Antyllus was just some guy who happened to be sacrificing, is even more precise, saying that those at the comitia fled. The dissolving of the comitia by rainshower is not nearly so comical as you seem to think--the Gracchans were the only ones left at the comitia, having driven everyone else from the area, and the presiding magistrates were able to halt the vote by invoking the sacral law that the comitia could not be held in bad weather. The city would take a brief breather for a couple days while battle lines were drawn before Opimius' faction, supported apparently by the urban plebs, launched a frontal offensive against the Gracchans. Similar tactics would be used in later years. Saturninus murdered his tribunician rival and was duly elected when his praetorian ally Glaucia assembled the comitia early the next morning by calling his underlings to the vote before the rest of the citizen body had assembled. Likewise, says Appian, during the vote on Saturninus' Gallic agrarian bill the urban plebs demanded the comitia be adjourned when Saturninus' thugs drove their opponents from the city--crying that they heard thunder the urban plebs were able to shut down the vote even though they had lost their physical presence at the assembly place. And later when Sulpicius drove his urban opponents from the Campus Martius during the proceedings around his tribal bill the consuls Sulla and Pompeius Rufus were able to close down the vote by proclaiming a holiday on public business.

That political violence was an endemic problem of the late Republic is abundantly clear, but it was hardly tolerated. Such public violence was said to have begun under the Gracchi, and the Romans believed that as political violence got out of hand eventually they turned into civil war. This is certainly true of some civil wars, such as Sulla's first march on the city, which was directly caused by Sulpicius' thugs driving him and Pompeius Rufus from the city, and in the case of others like Caesar's war urban violence, while not necessarily causing the war, was another outward result of the particular political pressures that would eventually cause armed violence. The Romans themselves acknowledged that they had had few ways to deal with such public violence besides meeting force with force. Both the Gracchi tried to violently force their opponents from the vote or intimidate them into not showing, and despite the attempt to legitimize Opimius' actions through the creation--for the first time--of the senatus consultum ultimum the fact remained that it was still fighting fire with fire. The execution of the Catilinarians managed to prevent outright violence in the city, although the threat was there in Cicero's gangs of armed equites, but in doing so Cicero was forced to violate laws against coercitio. Leges de vi tried, belatedly, to criminalize public violence, but were ineffective, and the Romans found that with no public police force comitia and trials in particular were highly vulnerable to violent offensives--by Publius Clodius' death it was found, for better or worse, that the only way to prevent mass rioting and attacks on Milo's trial was for Pompey to illegally occupy the forum with troops, who had succeeded in dispersing the riots of the night of Clodius' death by massacring the citizen body. Augustus did not permit such violence from ever occurring again, and his Draconian prohibitions on public and private meetings and establishment of military and paramilitary forces of public order, whose sole duty was to quell political unrest, were devastatingly effective in the decades after the civil war.

For the Romans of the late Republic public, political violence was the issue. It was a problem that increasingly could not be contained and to which all sides resorted when in a pinch. Generally speaking incidents of violence like that that the partisans of Gaius Gracchus began were met by a counterattack, and until relatively late these counterattacks were usually successful, if bloody. Only when Sulpicius drove Sulla from the city did a political leader have to resort to an actual army and civil war for the first time. By the 60s and 50s, when our documentation for public violence really takes off, public disturbances were endemic throughout the city. Clodius and Milo brawled with each other in the streets supported by throngs of hired (or perhaps not, although I believe that the evidence for the mobilization of collegia in the Clodian operae is quite poor) muscle, and there was fairly little anyone could do about it for a while. Senators were assaulted in the streets, public spaces (like the Temple of Castor) occupied or (like the forum, which Clodius dispersed with a muster of gladiators) had political opponents driven from them violently. In the case of Gaius Gracchus it appears that the Gracchans, who were initially successful, were not met with contrary violence for about a day--as the comitia, their entire purpose for clearing the assembly area, had been preemptively shut down they could not succeed in their purpose. But the citizen body, it is clear in our accounts, fled from the scene or were driven violently, and over the next day organized themselves under Opimius. This was not the end of a period of violence, but merely the beginning, a spark that soon erupted in full-scale political warfare. In other incidents the initial incident was met with equal force from the outset, such as the initial rioting during Sulpicius' tribal bill, and had to be broken up by whatever legal means were available--like many violent leaders, however, Sulpicius was not about to let the inability to pass legal measures stop him, and endeavored to press the attack for other purposes