The T-800 didn't really care about John
When John Connor reprogrammed it, he just had it pretend to gain human emotions so that his past self would trust him. Changes to history only ripple from when they started onwards.
Hence why Connor still exists when there's no SKYNET to eventually motivate him to send Kyle back to father him, and why they even remember the events of the 2 Terminator movies when the future can't prevent them going back in the first place. While the present changing the past does change the present(or else SKYNET's plan was All for Nothing), the present changing the future doesn't change the present even if those events directly led to the present they know. It also solves the potential paradox of if the original T-800 or the T-1000 won; the future would see no reason to send them back, but as the ripple effect only goes forwards it wouldn't affect them. Terminator Genisys supports this with T-3000 John Connor being an "exile in time" and able to pull off a Grandfather Paradox, by virtue of being under the same circumstances as John Connor preventing SKYNET existing in this movie. This makes the T-1000 even more of a gamble because if it realizes this, it would be wholly willing to turn traitor and warp SKYNET's history to its own liking or just Ret-Gone it and be independent without risk. The young, redheaded girl who informed the T-1000 of John's whereabouts was Kate Brewster.
Reprogramming the T-800 was a pivotal role in Future John's victory over Skynet.
The "Uncle Bob" T-800 possesses a lot of knowledge about Skynet and its operations. While it could've been filled in on the T-1000 from Future John, he has detailed files on Skynet's origins that are implied to just be part of his natural software. If information like this is stored in other T-800, either put there by Skynet or part of some Hive Mind like network Skynet is running, reprogramming them would be a serious information leak for the Master Computer. Connor was able to put the final nails on Skynet's coffin because he had insider knowledge about its methods from the advanced Terminator models. Why didn't Skynet consider this? It assumed that humans would hate machines too much to consider them possible of being reprogrammed. The resistance reprogrammed our T-800 hero to be less unsettling to dogs.
While James Cameron did it to avoid confusing audiences about the T-800's true intentions, it could be explained that the resistance had better human gait analysis knowledge and made T-800 appear natural enough to not alarm dogs. This was to prevent the ruse from being detected too easily in the past. The LAPD SWAT Commander was Hank Schrader
After the shootout at Cyberdyne, he would go on to join the DEA and move to Albuquerque