Dionysus: "All Asia is mine, […] But in the land of Hellas this city Thebes is the is the first place I have visited." (1)
In case you don't know, Hellas is another word for Greece. Dionysus is pointing out here that he's spread his religion all over Asia, but that Thebes is the first city in Greece to get a taste of his lively rituals. By Euripides's time, Dionysus was a considered a totally legit god, but back in the day, the religion probably seemed like a bizarre foreign invader.
Dionysus: Onwards! My women of Tmolus, you bulwark of Lydia, you, my sisterhood of worshipers, whom I led from foreign lands" (1)
The Bacchae is full of dualities and paradoxes. Here's one of them. Dionysus is the son of a Greek woman and a Greek god. Though he's Greek through and through, his religion and his battalion of followers come from Asia. In a way, Dionysus is native and foreign at the same time.
Chorus: "From the purlieus of Asia I come Deserting Tmolus the holy." (2)
The ladies of the Chorus have left everything they know for Dionysus. He's plucked them from their homeland on the mountain of Tmolus and taken them to a foreign land to spread their religion. The fact that they've come so far from home shows the depth of their devotion.
Tiresias: "He [Dionysus] is was who turned the grape into a flowing draft and proffered it to mortals; so when they fill themselves with liquid vine they put an end to grief." (22)
Interesting fact: wine is a foreigner to Europe. That seems strange, right? Europe is famous for its many different kinds of wine. It is a fact, though, that the grape is not a native fruit to Europe. It came from Asia way back in the day. The Bacchae is, in part, a celebration of that highly successful foreigner invasion.
Pentheus: "Foreigners have much less sense than Greeks." (54)
Pentheus here exhibits a common attitude in ancient Greece. He pretty much thinks Greeks are the smartest, most civilized people on Earth. We can't be too hard on him, though. We have a feeling that the people on the other side of the sea feel the same way about themselves, and think the Greeks are backwards and uncivilized. Suspicion of foreigners and the unknown in general is a pretty common human trait.
Leader: "Oh, let me shout my song in foreign tunes: a foreigner who need no longer tremble in fear of fetters." (220)
Now that Pentheus has been killed, the Chorus need no longer fear his persecution. Their foreign religion has conquered the over the stubborn Greek King.
Agave: "Bacchants from Asia, look!" (228)
This is the only time in the play that one of the Maenads, the Theban women whom Dionysus incites to worship him, meets Chorus, the god's Asian followers. It's interesting how Euripides places these two groups of women in contrast with each other. The Chorus worships Dionysus of their own volition, while the Greek women were forced into it. What does this say about the spreading of this foreign religion in Greece?
Dionysus: "I shall not curb the flail under which these culprits have to smart They shall be exiled from the city […] Not one of them shall ever see their fatherland again." (310)
Exile was a fate worse than death for most ancient Greeks. For many, their entire sense of self was based around whichever city they lived in. Perhaps, their suspicion of foreigners was heightened by their fierce loyalty to their own homeland.
Dionysus: "You [Cadmus] shall drive a chariot drawn by bullocks […] leading a barbarian tribe." (310)
Part of Cadmus's punishment is that he must lead an army of foreigners in a series of battles. Notice the use of the word barbarian here. To the ancient Greeks, most every foreigner was barbaric. It's extra humiliating for Cadmus to lead a group of people who he feels are inferior.
Cadmus: "an old man as an alien, his home in alien lands.[…] he must lead barbarian mongrel hordes against our Hellas" (319)
So, not only must Cadmus lead an army of foreigners in battle, but he also must lead them in attacking other Greeks. It really is a fate worse than death for they guy who founded Thebes. He's about as Greek as it gets, and now he's being forced to betray his own people.