Does Euripides challenge the tradition of Greek tragedy in The Bacchae?
This question is a bit difficult to answer because we don't know much about what previous tragedians had done with the story of Pentheus and Dionysus. Typically, though, Euripides is regarded as pushing the boundaries of Greek tragedy, especially in his portrayal of the gods, sexually charged and immoral women, his inclusion of sophistic thought, and his allowing people from the lower classes to play a greater role in his dramas.
Aristophanes' Frogs (405 BCE), which came to the stage perhaps a year before Euripides' Bacchae, brings up all of the above-mentioned issues. In that play, Aristophanes links Euripidean thought with Socratic thought. Furthermore, in Frogs, Aristophanes has Aeschylus and Euripides engage in a contest to see which of the two was the more useful poet for the people of Athens. In Frogs, the god Dionysus chooses Aeschylus as the winner because he thinks Aeschylus' play offers the people of Athens the sort of traditional, conservative teaching that made Athens great.
All that having been said, when we look at Euripides' Bacchae, we do not find women engaging in sexually immoral acts, although Pentheus thinks that they are. We do have a woman (Agave) killing her child (Pentheus), but it was not deliberately as in the case of Euripides' Medea. We do find sophistic language in many remarks of Dionysus, which does seem rather striking; although in Aeschylus' Eumenides (458 BCE), we can certainly find subtle speech in Apollo's argument for acquitting Orestes of the charge of killing his mother.
Dionysus is a rather complicated character, though, and by the end of the play any sympathy that he might have generated in the play's first half seems to have largely disappeared. Pentheus may have denied the god's power, but Dionysus utterly humiliates him and completely destroys him, having Pentheus' female relatives literally tear him apart. Even the Chorus, comprised of Dionysus' worshippers, show some sympathy for Cadmus after his grandson's death: "I'm sorry for you Cadmus—you're in pain" (Ian Johnston translation).
Finally, students often seem bothered by Dionysus driving Agave, Cadmus, and Harmonia into exile. To have a god behaving in such a cruel fashion certainly seems thought-provoking and perhaps challenging to the boundaries of Greek beliefs. As Cadmus says, "Angry gods should not act just like humans" (Ian Johnston).
Thus, if a student is looking for a character in the Bacchae who challenges the tradition of Greek tragedy, I would imagine Dionysus would be a "good" one to examine.