The "right thing" is surely fixed, but the morality of what to do to get to the "right thing" is going to change from person to person, scenario to scenario, belief system to belief system.
For example, this morning the "right thing" is that I get my child to nursery. There's no real moral decisions to make there except maybe to I walk or drive? Usually I'd say morally I should walk, because it's better for her health and the environment. But as we recently got a new puppy, it's better than this time I drive so the puppy isn't left alone too long for the first time. It won't hugely impact DDs health or the environment if today I drive but it will hugely impact the puppy's ability to be left without stressing if I take longer by walking.
The "right outcome" is still achieved, my child ended up safely at nursery. But other people will have different ideas as to whether I was morally correct in how I did it.
And then you have things the other end of the scale, deciding whether to join conflicts in other areas of the globe. The "right thing" is that those end, but morally, what's the best way to do that? Do we join fights? Should fights have started in the first place? How should they have been prevented?