I think @FelixGoldberg has the core of it; the source is not reliable or useful. Somewhere in one of Asimov's robot novels he has a comment about reasoning based on flawed sources & assumptions, and I think the wikipedia quote in question falls into that category.
The best I could find is the following: Apparently Porcius Festus was the least offensive of a series of procurators.
It is fair to assert that the procurators were either openly hostile or, at best, indifferent to the needs of the Jewish populace. They were notorious for their rapacity. Their relatively short tenure, coupled with hostility toward Jews as a whole, may have impelled them to amass quick profits. Whatever the case, the last two procurators before the Jewish War (66 C.E.), *Albinus and Gessius Florus, as a consequence of their monetary extortions and generally provocative acts, were indubitably instrumental in hastening the outbreak of hostilities. The only exception appears to have been Porcius *Festus (60–62 C.E.) who made vain attempts to improve conditions. Jewish Library
One commenter has pointed out that the source may have a bias. Most of the sources I consulted have similar facts, but most of them share the same underlying interest - Jewish history. I doubt that Festus was that important in Roman history as whole.
In my comment, I mentioned my hypothesis that monotheism might have been the cause of the dispute. OP indicated that I needed to clarify. In a polytheistic society such as Rome, monotheism is very suspicious. Rejection of societies shared gods implies a rejection of societies shared values and foundation. If the Jews reject Roman values, then implicitly they must not be far from rebellion. The issue wasn't that the Jews were upset by monotheism, but that the Romans were suspicious of people who rejected Gods, Virtue and laws (the concepts weren't entirely distinct).
Update - searching on the term "civic privileges" suggests that the term may be analogous to what we now term "civil rights". Viewed in this light, Festus didn't create civic privileges, but inherited the problems that are presented by the Romans granting civic privileges to Jews. If Jews had no civic privileges, but were viewed as an alien tribe, then they effectively had even less rights than slaves. Granting them civic privileges meant that some fraction of Roman legal and jurisprudential tradition applied to the Jews. The Jews on their part were perceived as not fully participating (they could not serve in the army without participating in forbidden rituals, they refused to worship the state gods, etc.)
* Rome, Regal and Republican (warning; links to google books have been sketchy in the past) discusses the civic privileges of the libertini.
Heritage History provides the following quote:
It is also a remarkable instance of Roman respect for established usages that notwithstanding the rebellious disposition of the Jewish community in different parts of the empire, the Romans continued to allow the Jews to retain their civic privileges in all those cities where they originally possessed them.
A Companion to the Roman Republic contains the phrase:
Assimilation to Roman ways sufficed to authorize the award of full civic privileges
The Roman Republic: A Very Short Introduction
Capua and Rome's other Italian allies again had to provide men for military service in return for Roman protection and a share of the plunder, but also had to pay a set annual tribute and received fewer civic privileges.