I've mulled it over some more, and I still believe there has to be a timeline where someone other than Kyle Reese is John Connor's father. When The Terminator was a standalone movie, you could read it either way. Either there's a circular causality, where Kyle is "always" John Connor's father, or Kyle's time travel creates a new branch. But Terminator 2 pretty much establishes that time travel always creates new branches, because there's no fate but what we make. And the Connors, with their friendly T-800, are able to stop or at least delay Skynet. But of course, your mileage, even backwards and forwards through time, may vary.
Link -via reddit