I think the one rule of time travel should be: "You can't change your own past, but you can change other people's futures." In other words, anything that happens in the time loop has to be explainable back to a source event that maybe gets modified into a reinforcing loop, and maybe not. It doesn't matter. What matters is that everything starts somewhere.
Let's take Terminator. In the beginning, man created Skynet. Skynet fought man, and man fought back. Skynet sent a Terminator back in time to try to kill the mother of the leader of the resistance, who happens to be Sara Connor, and that leader sent Kyle Reese back to prevent that from happening.
Kyle Reese fathers John Connor after succeeding in defeating the Terminator and then dies. John Connor grows up, taught by Sarah Connor to prepare for the coming apocalypse. Man creates Skynet. Skynet fights man, and man, led by John Connor, fights back. Skynet sends a Terminator back in time to kill Sarah Connor, and John Connor sends Kyle Reese back to prevent it from happening.
Now you have a tight, self-reinforcing loop: Kyle Reese -> John Connor -> sends Kyle Reese back in time -> repeat. You also have a plausible entry into that loop, in that the John Connor we all know about is not necessary to start the loop, only some offspring of Sara Connor. Maybe trained by a survivalist white supremacist or ex-army-ranger something stupid.
So. That's all plausible in ways that Genesys isn't.
Let's hand-wave aside that some random person in the future (beyond Reese's departure, after Connor's subjugation by Skynet-II) sent a terminator back in time to prevent another terminator (sent by who? when?) from killing nine-year-old Sara Connor.
Where does Skynet-II originate? At what point, during what iteration of the loop, does Skynet-II get created? It must be through John Connor at some point, because Skynet-II sees Connor as the key to its own birth. But in the loop iteration where Skynet-II is born, John Connor isn't born when he was the second time through the loop (post-1984).
Similarly, there's no point in old-Reese going back to see his 2017 self because now that the time loop has been exited, there's no reason to propagate the event into the next loop. All that matters is that it already happened -- which it clearly did. It doesn't need to happen again.
Time travel affecting the past which affects the future is fine. You just have to have a plausible entry into the loop for it, and Genesys just doesn't have that.
But if you ignore all that, the movie delivers on blowy-stuff-uppy.
