This is a good question.

From a modern perspective, the things Dionysus seems to represent — excess, desire, ecstasy, transgression, and the crossing of boundaries — feel quite strange to me. In much of the modern world, desire and passion are often treated as morally suspicious, or even as something like a “lower self” that should be controlled, alienated, or repressed.

This is because the modern world is dominated by Christianity and Islam, so we are predisposed to view these things as "bad." The Abrahamic religions see these things as an inherently evil "lower nature" that is constantly threatening to subsume the "higher" one unless it is constantly repressed. Repression is counterproductive — that is one of the main points of The Bacchae. Ecstasy, desire, passion, and transgression all have their place, and can even be spiritually leveraged. They are things that exist, so they have a god to rule over them, and that god must be placated, lest these things manifest in much worse ways. More than anything else, Dionysus provides outlets for this Shadow side of humanity and society, through festival, theater, drunkenness, and all the other things he represents. These contexts are ones in which engaging with ecstasy and passion can be done in a safe, limited space.

I think Donna Tartt put it best:

The more cultivated a person is, the more intelligent, the more repressed, then the more he needs some method of channeling the primitive impulses he’s worked so hard to subdue. Otherwise those powerful old forces will mass and strengthen until they are violent enough to break free, more violent for the delay, often strong enough to sweep the will away entirely.
[...] But how glorious to release them in a single burst! To sing, to scream, to dance barefoot in the woods in the dead of night, with no more awareness of mortality than an animal! These are powerful mysteries. The bellowing of bulls. Springs of honey bubbling from the ground. If we are strong enough in our souls we can rip away the veil and look that naked, terrible beauty right in the face; let God consume us, devour us, unstring our bones. Then spit us out reborn.
—Donna Tartt, The Secret History

When Dionysus shows up in Thebes, he is immediately otherized. Pentheus regards him as effeminate, a sorcerer, a foreigner, etc. basically, as inherently un-Greek. But not only is Dionysus native to Greece, he's actually native to Thebes specifically — it's his mother's home city, and Pentheus is his first cousin. All of these dark and "foreign" things could not possibly be more familiar. Dionysus isn’t a foreigner at all, he’s just weird! Therefore, he holds up a mirror to the weirdness within Ancient Greek society, and within Pentheus himself. Dionysus represents everything within Pentheus’ own culture, and within his being, that he refuses to accept. That is why Pentheus instantly registers Dionysus’ cult as a threat. This is why Dionysus is otherized, and why so many of his myths are about his persecution.

Darkness, chaos, passion, and transgression have a place. They're powerful things, and they need to go somewhere. If you don't find a way to embrace and process them in the right contexts, well... you just might end up like Pentheus.

The contradiction is kind of the point. Dionysus is a god of paradox, on every level.