When you talk about the effect this play had on society, you have to think of the different societies in which it was performed. The play was first produced in Copenhagen, Denmark, where sexual mores may not have been so strict as in other countries. Other European nations banned public performances of the play; the eNotes introduction tells us that Britain did not lift the ban until 1939.
As for attitudes toward women during this time, it is important to note that the main focus of this play seems to be class differences. Julie is an aristocrat who has an affair with her servant. However, she becomes subordinate to him by allowing him to insult her. The Historical Context section notes also that
The position of women in society was also an important issue at this time. It was only in 1845 that women in Sweden were given the right to own property. In 1846 women were also given the right to hold certain specific jobs, such as teaching, and finally, in 1862, the right to vote. In the 1870s, women were let into the universities for the first time, although they were not allowed to study theology or law. In general, women were gradually becoming, at least in the eyes of the law, more independent and closer in equality with men.
It is important to know the role of women in the time this play was written, but it is also important to explore class distinctions.