Seleucus, one of Alexander's officers, took Babylon in 312 BCE and built from it an empire that at its height reached from the Aegean to the Hindu Kush. Its instrument of rule was the city: dozens of new Greek foundations, Antioch, Seleucia on the Tigris, Apamea and the rest, planted with settlers, temples and gymnasia, and Paul Kosmin's study reads the whole imperial project as an argument about space, an attempt to make a conquered continent legible as a homeland.
The dynasty's religious posture was double and deliberate. To Greeks the kings offered Olympian cult, dynastic worship and the identification of local gods with Greek ones; to Babylonians they presented themselves as legitimate Mesopotamian kings. Antiochus I's cylinder from Borsippa, written in Akkadian in the old royal formula, records him rebuilding the temple of Nabu and moulding its first brick himself, and the Seleucids continued to fund the great sanctuaries of Babylon and Uruk, where cuneiform ritual texts were still being copied under their rule.
Toleration of this kind was ordinary Hellenistic practice and cost the dynasty nothing. Local cults kept their revenues and their priesthoods, provided they acknowledged the king; the empire's religious policy was, for most of its subjects and most of its length, a matter of patronage rather than pressure. What happened in Judaea in the 160s BCE was therefore an anomaly, and it is argued about precisely because it was one.