The theatre was very important for the Greek culture, it was a way of transmitting the myths of the Greek Ancestors and their beliefs. Also, I think that it was an easier form of protest, an easy way of share subliminal messages that many Greeks could understand. At the same time, keeping the audience entertained. Euripides aim would have been to explore the behavior and the relationship between the Gods and humans even if he does not honor or judge the God Dionysus at all. Also, it sees the human side of the God that it makes him feel inferior in comparison to other Gods.
A curious theme of that period was women, as they were not taken into consideration in the Ancient Greece, they were not able to perform on the stage and their roles were performed by young boys. However, it did not undermine the role of women in Greek plays. The Bacchae is a women tragedy full of women doing unusual things from different sexual aspects. We can link it with the resolution of the play where Agave is possessed by madness to lose her self-control and does not recognize her son. Another important aspect of the play was the King Pentheus who got convinced by the priest to dress as a woman this way losing his dignity.
Also, the final message that I got from The Bacchae is that Euripides tries to expand the religion making people loyal to their faith and myths of how no one can deny a God. Aristophanes wanted to help making a change in the political arena, enabling people to think through his comedies. Both of the styles comedy and tragedy are political as I think all theatre is political. I believe that any theatre performance has been made for a reason it can be for a purpose as change the vision of the public, a way of entertainment or to leave the conclusions and the meanings to the public as individual.