Forget everything but the basics. The cast that you know and “love” doesn't exist in the this universe and their stories are just as absent.
Here, the Quincy and Shinigami have reached an uneasy truce after a brutal war that has wiped out generations. Caught in a political stalemate, both sides are unable and unwilling to risk outright warfare any longer. The ill-feelings are still there, though, for the horrors and wounds of the Spirit War live. While publicly, “tolerance” is the buzzword, “annihilation” and “genocide” are choice flavors for blood-thirsty tongues. New and Old Blood on both sides have indulged in its taste and the results are "accidents" and "misunderstandings" that end in dead bodies littering the streets, towns being wiped off the map and chaotic power-plays within their own ranks.
Look past beyond this and see how these struggles spill over into the Living World. The increased presence of spiritual energy has granted otherwise normal people powers. Many of them have no idea what do their newfound abilities or how to control them, but it changes their lives drastically and sometimes horrifically. Every day, children are born with the ability to sense and manipulate this other plane of existence, but the chances are still so rare that it is they need to find inner strength for support cannot come from those that don't understand.
While this Spiritual Cold War mostly been kept between the Quincy and Shinigami, it is not unknown for living humans to be dragged into the fray and death isn't peculiar about whether to take the young or old into their graves. The humans, typically not as powerful as the other two spiritually adept factions, are the most frequent targets by the terrifying beasts that cross the spiritual barriers. Stretched thin as it is, the Shinigami and Quincy are unable to protect them as they once were. In the night, one can hear the blood-curlding screeches of a hunt started anew.
From the distant sands of Hueco Mundo, the Hollows have never known a greater feast in their dismal lives. The injured and dying make for easy meals and the gnashing teeth easily devour choice meat. The less evolved have noticed no difference between the Spiritual War and this Age of “Peace”, so they frequently breach the barrier into the Living World and Soul Society. They see no difference between the Quincy, Shinigami or Humans and they throw themselves with unquenchable hunger. They are not the worst.
The worst lies in the Hollow that have become strong and smart enough to know what is going on. They know that the Shinigami are weakened, the Quincy are desperate and the Humans unskilled. There are rumors that these monstrosities have become the generals for the masked hellspawn and it is only a matter of time until they abandon their desolate sands and bring a reign of flesh-devouring horror to the other worlds. Yet, while having the advantage, there are still things these Hollows are concerned about.
The mysteries of this universe are numerous, but of the most important ones are the rumored vizard and arrancar. While it is known what they are and the danger they pose, it is not known how they came to be. Hybrids, they are typically feared and banished from the those they once called friends, family or packs. Abominations, there is not a group that will publicly align themselves with these outcasts, but it is rumored that a few have been employed before unofficially.
This is the world that you have stepped into. Be wary of both your allies and your enemies. Be prepared to defend your life and those that you love at any moment for the world is a brutal place.