Answer:
Religion, although nowadays much disregarded as central to human life, was the epicenter of it in ancient times. And nowhere is that clearer than during the centuries in which ancient Babylonian cultures, one of which was Sumer, appeared.
Sumer, as said, was part of the greater Babylonian culture and they, like all the other Babylonian civilizations, were grounded by politheistic religion. Essentially, they believed in multiple divinities, which were really human-like, and who were responsible for controlling parts of human life, and the world itself.
First and foremost, religion shaped the way that Babylonians, and especially Sumer, believed. Their actions, behaviors, thoughts, everything, revolved around their beliefs in these deities. Religion also dictated social lifestyles, communication, and politics.
Finally, and most importantly, religion shaped the way that Sumer developed both socially and politically. Politically because initially the rulers in Sumer were priests, and for a very long time they were the ones who led Sumerian people. This tradition was later passed on to other civilizations which came in contact with Sumer, and with Babylonian civilizations. Second, when ruling was passed on from priests to kings, Sumerians believed that these kings were elected by the gods, and were representatives of the gods, and therefore, they believed in the divine intervention of deities on all aspects of their lives.
These are only a few of the ways in which religion shaped not just Sumer, especially on governmental aspects, but in other aspects of life as well.