There are many themes in Euripides Bacchae. It is a wonderful work that deserves to be read several times.
Let me only name a few of themes. First, I would say that one of the most important themes is religion. Dionysius, the figure that is in view in the work is a god. This point is important to remember. The Greeks believed that the gods must be worshipped properly. We can say that there were very religious.
Second, in connect to this point, the properly devotion to the gods is important. This is where Pentheus made his very fatal flaw. Instead of worshipping Dionysius, he confronted and challenged him. To the Greeks, this was seen as hubris. In other words, Pentheus transgressed his role as a human and challenged someone divine. In the Greek mind, he did not know himself. Remember the oracle at Delphi stated, "know thyself!"
Third, if you recall the devotees of Dionysius were women. So, another very important theme is the role of women in the Greek world.
Here are some key points in The Bacchae:
RULES can STIFLE
The Bacchae warns people that following rules too striclty can be harmful for society. Rules have their place, but they can also be stifling. In the story, King Pentheus tries to constrain and contain the will of the god Dionysus. As such, the King, the city, and the entire populace finds life much harder. Even though things weren't perfect before the rules, the rules themselves cause more harm then the imperfect chaos which existed before.
The theme of insanity plays out in multiple ways and in mutliple overlapping plots. Dionysus can induce insanity in people to the point of extreme violence and debauchery. On the other hand, as we see in the laws/rules that King Pentheus tries to impost, a lack of insanity can also be a bad thing. Some critics have pointed out that one of the main themes of the play is that the rational and irrational, the sane and the insane, the mad and the calm need to co-exist. Too much of either isn't a good thing.