Obviously he hasn't actually stopped caring. No one, at least I hope no one, literally thinks that he magically stopped caring in that fight scene with Zod. No one has actually made that argument.
The problem they have is that in that scene, he doesn't show any concern until they land in the train station. Yes, Zod's genocide plan was a nightmare to him. Yes he has been established as someone who cares. And yet in the fight with Zod he doesn't show any concern for the collateral damage the fight is causing. It's inconsistent, it betrays the artifice of filmmaking, and it makes people feel like he doesn't care. Yes, logically, we know that he should care, but a big part of movies is how information is presented to the audience and how it makes them feel. If you have to go back and say "Well, he clearly was opposed Zod's plan so even if he didn't seem like he cared in the Zod fight logically he must still care" then the movie isn't doing it's job properly.
Really, the fact that they established him as someone who clearly cares earlier in the film proves my point, not yours. If it makes us feel like he doesn't care when it's been established that he does, then the movie ****ed up.