A quick hypothetical...
A completely insignificant male human named James in 65000001 BC encounters a gate to 2300 AD. He enters the gate and winds up in 2300 AD. Which version of 2300 AD does James see? (Ignore Crono Cross)
Now if you're going to complain that you don't have enough information to predict which version of 2300 AD is the correct one, this means that you need knowledge of what time travel has taken place between 65000000 BC and 2300 AD. In other words, does James enter the gate before Crono kills Lavos? I think that question doesn't make any sense. James isn't aware of Crono or Zeal or whatever. Everything that Crono does is in James's timeline's future, chronologically.
We know what 2300 AD is like "before" Crono kills Lavos because we're following Crono. But in my hypothetical, we're following dumb, ignorant James. What does he see in 2300 AD?
My answer? Well, if I strictly follow the time travel mechanics of the game, as I interpret them, then James ends up in the "final" 2300 AD, the bright sunny future of a slain Lavos. It's impossible for him to see the ruined future we've seen because all of the time travel that makes up Chrono Trigger's plot happens in his future. The cast of Crono never venture before 65000000 BC. So I think this has be a general rule, and one that's consistent with the storytelling of the game. You can never see a timeline that's been destroyed due to time travel taking place in your future.
What do you think? Is this obvious? I started this rant intent on proving that, with Crono Trigger's time travel rules, determinism must exist. But now I think the opposite is true.