Art by chiyahowo on Tumblr
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Past Dream (from the very beginning of the SMP when he was good and thought of Tommy like a little brother) is sent to or is shown the future and he gives himself one goal: to stop the future from coming true and protecting Tommy, Tubbo, and eventually, Ranboo, at all costs. He is disgusted with what he is supposed to become, and decides to spit in the face of his future self and carve his own path, not from blood, but from peace.
He allows L'manburg to form and doesn't start a war. He keeps Schlatt from becoming too powerful and puts an end to his tyrannical rule as soon as it starts. He supports Tommy when his shit family (Techno and Phil) rear their ugly heads. Basically, Big Brother Dream finds out about his future and punts it, adopting Tommy in the process.
If Dream is instead sent to the future, it would probably be to the start of the L'manburg War of Independence. It would probably make more sense if he already knew about the future before he was sent there, otherwise I think he'd side with himself in the war. Knowing how the future is though, Dream takes his mask off and introduces himself as Clay, joining the L'manburg side of the war. Because he's, y'know, DREAM, he helps them win. (To prevent confusion between Dreams, from this point onward Future Dream will be Dream and Past Dream will be Clay). Dream is confused, startled, and a little bit afraid at the fact that he's fighting himself, and confronts Clay as soon as he can.
Clay tries to warn Dream of what's to come and that he needs to stop, but Dream is in denial and continues to spiral. Clay then lives in L'manburg and devotes himself to keeping the Clingy Duo, eventually Bench Trio, safe and stopping Dream. He's there for all the major events that still happen (Clay stops most of them) and protects whoever he can. I think certain things that are a direct result of Dream manipulating people, like Wilbur going insane and blowing up L'manburg or Tubbo exiling Tommy, just don't happen because Clay stops him. He becomes infamous around the SMP for protecting the minors and being kind and polite, unlike most of the SMP.
I think it'd bee cool to have a scene where Clay reveal to everyone that he's from the future and there to stop something terrible. Maybe he also hands out warnings to people, like Technoblade in Pogtopia, or Wilbur about the elections.