I'm referring to this particular passage:
Even when polytheists conquered huge empires, they did not try to convert their subjects. The Egyptians, the Romans and the Aztecs did not send missionaries to foreign lands to spread the worship of Osiris, Jupiter or Huitzilopochtli (the chief Aztec god), and they certainly didn’t dispatch armies for that purpose. Subject peoples throughout the empire were expected to respect the empire’s gods and rituals, since these gods and rituals protected and legitimised the empire. Yet they were not required to give up their local gods and rituals. In the Aztec Empire, subject peoples were obliged to build temples for Huitzilopochtli, but these temples were built alongside those of local gods, rather than in their stead. In many cases the imperial elite itself adopted the gods and rituals of subject people. The Romans happily added the Asian goddess Cybele and the Egyptian goddess Isis to their pantheon. The only god that the Romans long refused to tolerate was the monotheistic and evangelising god of the Christians. The Roman Empire did not require the Christians to give up their beliefs and rituals, but it did expect them to pay respect to the empire’s protector gods and to the divinity of the emperor. This was seen as a declaration of political loyalty. When the Christians vehemently refused to do so, and went on to reject all attempts at compromise, the Romans reacted by persecuting what they understood to be a politically subversive faction. And even this was done half-heartedly. In the 300 years from the crucifixion of Christ to the conversion of Emperor Constantine, polytheistic Roman emperors initiated no more than four general persecutions of Christians. Local administrators and governors incited some anti-Christian violence of their own. Still, if we combine all the victims of all these persecutions, it turns out that in these three centuries, the polytheistic Romans killed no more than a few thousand Christians.
Furthermore, if Romans really took exception to strict monotheism of early Christians why were they able to be tolerant of Jews and their, presumably equally as strict, monotheistic worship of what is ostensibly the same god.
The first hundred or so pages of Paula Fredricksen's Augustine and the Jews (London: Yale University Press, 2010) expands greatly on the idea that in the ancient world, gods were "local." Everyone owed allegiance (usually in the form of cultic ritual--offering sacrifices, burning incense, etc.) to "their" gods: the gods of their ancestors, the gods of whatever place they lived in, and in the case of the Roman Empire, the gods of conquering armies.
Most people in the ancient world were polytheistic; as long as they worshiped the gods they were required to worship, they could worship others as well. So if you lived in Ephesus, you had to appease Diana of the Ephesians. But if your ancestors were from Syria you might have obligations to those gods as well. No problem; just worship all of them.
If you didn't meet your obligations to the gods, and things started to go wrong--famine, flood, drought, earthquake, volcano eruption-- then blame was laid on anyone who had not properly kept the peace with the gods. Cultic worship was mandatory in order to keep this peace, and this worship was enforced through cultural pressure and the power of the state.
To say that the Romans saw Christians as political subversives is not entirely wrong, but it is important to note that distinctions between what we might call "nationality" (an anachronistic term, see Benedict Anderson's Imagined Communities [New York: Verso, 1991]), "ethnicity," and "religion" are not so easy to maintain when we study the ancient world. Today you can be a Buddhist Korean American. In the ancient world, you worshiped the gods of your ancestors and the gods of your land or city. To worship the gods of some other people or some other land while eschewing the gods to which you properly owed worship could easily have been seen as aiding and abetting the enemy, so to speak. By refusing to burn incense to Caesar, the Roman authorities would have understood the Christians to be stating that Caesar was not a god (which was a correct assessment of Christian belief), and also that they (Christians) did not recognize Caesar as their political authority (which was not necessarily correct). The ancient world did not really have the categories to distinguish between one's national-political-cultural-ethnic responsibility and one's religious or cultic responsibility. To reject the latter was to reject the former. Fredricksen has a name for this idea: "cultural treason" (Paula Fredricksen, "What 'Parting of the Ways'? Jews, Gentiles and the Ancient Mediterranean City," in The Ways That Never Parted, ed. Adam H. Becker and Annette Yoshiko Reed, 42).
So to answer your question, "theological difference" and failure to pledge political "allegiance" are not totally different ideas. Abandonment of one's "religious" responsibilities was by definition also abandonment of one's civic duty.
As for your second question, Jews were exempt from the imperial cult due to a longstanding agreement beginning with Caesar's decree that Jews should be allowed to continue in their ancestral customs as long as they paid the appropriate taxes (Josephus, Antiquities 14.10). The Jews had helped the Romans in the Alexandrian War, and their beliefs were ancient and ingrained; Caesar seemed favorably disposed enough to leave them to their own customs. As later emperors began to demand to be worshiped, the agreement with the Jews was generally still honored (Caligula attempted to break it, but failed), and Jews were not required to participate in the imperial cult.
Because most Christians were not Jews, they did not fall under this exemption. Magnus Zetterholm in The Formation of Christianity in Antioch: A Social-Scientific Approach to the Separation Between Judaism and Christianity (London: Routledge, 2003) argues that non-Jewish Christians attempted to convince the Romans that they, and not the Jews, were the true inheritors of the heritage of Abraham and therefore deserved to be exempt from the imperial cult. The Romans did not buy this argument. Furthermore, the Jewish community pushed back by distancing themselves from the Christians, intensifying Roman scrutiny of this odd sect that claimed to be in some sense "the real Jews" but were obviously not Jewish and had not converted to Judaism.