Was babylonia society at this time monotheistic or polytheistic

It depends on what era you are referring to.
In the beginning, the Babylonian society was polytheistic, meaning that the people believed in many gods. In Babylonian religion, there were over 2,100 gods whom people worshiped, such as Ishtar, Sin, Nergal, etc.
However, later in the day, when Christianity started spreading in the area, it became monotheistic.