Source: Peder Borgen, "Philo of Alexandria," Jewish Writings of the Second Temple Period, ed. Michael E. Stone (Philadelphia: Fortress, 1984) 253-254.
"By joining in cultural life, the Jews of Alexandria aimed at full citizenship of the Greek polis...Full Greek citizens were exempted from the Roman poll tax, the provincial Hellenes paid a lower rate, and native Egyptians paid the tax in full. The Jews in Alexandria pressed for equal status with the Greeks there. The Greeks in turn, tried to deprive the Jews of the privileges granted by the Emperor Augustus, and have them classified with the native Egyptians. After Gaius Caligula became Emperor in 37 C.E. these quarrels in the religious, cultural and juridicial field led to anti-Jewish riots which grew into a pogrom. A military uprising by Jews against Greeks followed in 41 C.E. on the death of Gaius Caligula and the accession of Claudius."
There's a lot that I don't know about this situation, and I'm sure Philo's treatise spells things out a lot more. Part of me wonders why the Jews didn't simply pay the tax. They claimed that they were persecuted, when it seems they were just deprived of citizenship, as were the Egyptians. Not being put in the elite is not the same as persecution.
At the same time, the pogroms were persecution. I'm not sure who carried them out. Were they the Greeks, or the Egyptians? Did they do this because they thought the Jews were just plain weird? Or did the Egyptians dislike how the Jews were trying to get a higher status, something they (the Egyptians) could never attain?
One thing is certain: the Jews felt persecuted. If the Wisdom of Solomon is from the first century, then it indicates that Jews in Egypt at the time believed they were oppressed on account of their religion. That's why they clung to the immortality of the soul and the justice God displayed at the Exodus.