When we talk about some people being morally better than others, there are two things we could be thinking about: their moral value, and their moral acumen (how accomplished one is in doing the right thing). Moral value is about a person’s worth. It’s what people are invoking when they say that members of one caste or clan or race or even hair color are superior to the members of another. Moral acumen is about a person’s judgment. It’s what people are invoking when they say that murder is worse than jaywalking or when they encourage someone to be the bigger person.
If the question were about moral value, I would agree with @KNOWITALL that we are all morally equal. No person is worth more than another, even if we are not all equal in strength, size, intelligence, or ability. But I take it this is a question about moral acumen and will answer it accordingly. In short, I think we are morally mature when we stop needing external reasons to be kind or friendly and not to be cruel or hostile, and I am more than a little concerned by people who say that the only thing holding them back from committing certain terrible acts is the fear or punishment and/or judgment.
I would also like to note that nearly every moral theory, whether of religious or secular origin, agrees that doing something because it is the right thing is morally superior to doing it out of a desire for rewards or a fear of punishments. While it is true that many religions tell you that there will be a punishment for doing the wrong thing, and while those may be used as incentives to get on board with their moral program, they also expect people to grow beyond those initial motivations.
So while there are certainly religious people who say things like “the only reason I don’t murder people is because I will be punished after I die,” they are mostly just exposing themselves as being in the early stages of moral development. And I suspect that their fellow believers who are further along the path are just as concerned about them as I am.
As for why we might care about someone’s motivations for doing the right thing: a person who does the right thing for the wrong reasons fails to do the right thing when their reasons aren’t satisfied. A person who does the right thing for the right reasons is far more reliable and serves as a better foundation for a moral community.