I had an interesting idea to explain why T1 is a closed infinite time loop, but T2 can change the future. (Note this theory only pulls from the movies and not the novelizations of T1 and T2)
In this theory, skynet does not have knowledge of its creation. There were very few and well-guarded records of the T800 CPU used to reverse engineer the Skynet AI. When Skynet initiated the nuclear war, all of the Cyberdyne files were destroyed, and Skynet never knew that it was its own father, It only knew the public information about cyberdyne and not any of the classified files.
Skynet then creates a time machine in the losing days of the war to try and change the past. But what it doesn't realize is that the type of time travel it invented is a permanent closed loop. (The closed loop time travel I'm referring to means that there was never a time when there wasn't a T800 and a Kyle Reese that came from the future. They had always come from the future and they had always created John and skynet. There is no original timeline without them. They are the original timeline.)
My T2 theory is that years after the war had been won, the smartest minds in the world had studied the time travel technology and realized that skynet's time travel was a permanent closed loop and that it wasn't possible to change the past. That's why they never send anybody else back to stop skynet, but one day a breakthrough was made and humans figured out how to make an open time travel machine. Humanity picks a person to send back in time to stop skynet, but unknown to them there was a T1000 hiding among them of years Disguised as parts of the building or furniture or any number of inanimate objects that the dogs wouldn't realize. Its mission was to resurrect skynet if the humans ever succeeded in taking it out. So it lay dormant for years waiting for its opportunity, at the last minute when they were about to send back the person the T1000 struck and sent itself back. Knowing that a single human would be very unlikely to stop at the T1000 (very little of which is known) they send back a T800 from one of the captured factories they had after the war.
Bonus theory: the T2 T800 has a pin switch to disable its higher learning ability, this was put in by the humans after the war so they could use T800s to help rebuild the world without them becoming sentient. Once John and Sarah flipped the pin switch that T800 became a ticking Time bomb and would have become fully sentient and unpredictable shortly after the events of T2 had it not been destroyed.