If karma is objective, how come it's cause for "good" rebirth?

A "good rebirth", or more precisely rebirth in a beneficial destination (sugati), is good because it is conducive to liberation. It seems to me that you are defining "good" and "bad" in decidedly non-Buddhist terms. Likes and dislikes contribute mainly to suffering, not to happiness. And the view that likes will make you happy is the main wrong view Buddhists are trying to correct.

Being rich, for example, sounds like a bad rebirth since too much wealth can get in the way of intention to practice, because you'll spend all your time indulging your likes and dislikes. Though there are one or two notable exceptions to this in the traditional legends, like Anathapiṇḍika for example who gave all his wealth to the Saṅgha.

As far as Buddhism is concerned there is only one really good state to be in and that is nibbāna, and that does not involve rebirth (punabhava). So any life in which the conditions are good for ending rebirth are "good" conditions.

There's another view of Karma that's more "objective".

Karma = the motivations for your actions. These motivations have nothing to do with "good" or "bad" actions, but rather whether you're acting out of attachment or non-attachment. Your actions will strengthen or loosen your attachments, and your attachments when you die govern whether you're reborn or not. If you're reborn, you're reborn with your attachments at death.

Since attachments = suffering, the quality of your new life has nothing to do with your material conditions. It doesn't matter if you're born rich or poor, beautiful or ugly, healthy or diseased. Die with a lot of attachments and you'll suffer more in the next life because of those attachments, and vice versa.

In short, Karma doesn't determine the quality of your birth by some decision made based on whether you were "good".

Full Disclosure: I treat Buddhism as a philosophy and thus don't believe in Karma or any other metaphysics. However, I encountered this view of Karma previously and felt I could contribute it despite my beliefs.

I think you might be getting hung up on the idea of neutrality. Karma isn't a system of divine justice dolled out by a celestial being. It isn't vindictive or rewarding - karma just is. You might want to try to understand it as a kind of natural force like gravity or electromagnetism. Karma is "neutral" in the same way. For instance, we don't go about our days worrying about offending gravity! Of course, we certainly know that if we decided to jump off of a building, we might not like the result.

I think the second sticking point here is a very common one - namely that karma has anything to do with good and bad. Jayarava Attwood touches on this in his answer, but I think it can be taken a step further. You have to remember, karma literally means action. The Buddha's great discovery was that correct action (of which right action - samyak-karmanta - is a part) had nothing to do with expressing your caste as in the Brahamanical system of his day. Instead, right karma were those actions that expressed virtue and renunciation. These actions lead to better conditions in this life because they create a kind of moral momentum. The same deeds become easier the more often they are done. They also help people arrive at better life circumstances. You see this all the time in individuals who change their behavior and suddenly find their relationships going better and their general lot in life improving. From life to life, good karma can also result in rebirths were enlightenment is easier to attain (i.e. the human realm). Obviously, it works the same way for negative karma.

So to sum up, yes karma is neutral but just as a balanced scale will tip if you add too much to one side, karma does reflect those actions that one is putting their volitional weight behind.

A good birth

A good birth is not about physical wealth.It is actually about mental potential and health.

(A)- Imagine you are a rich man

(B)- Imagine you are a dog in a rich man's house

(C)- Imagine you are a Poor man

(D)- Imagine you are a dog in a poor man's house

As you can see option (A) is good,but why

Buddhism has a signature and it is always referring to the path to nirvana. So the "Good" here is the man in option (A) can easily do many good things when the man in option (C) would have to go through many obstacles in life. The dogs have no potential so obviously it is a bad birth.

Now consider this

(A)- Imagine you are a rich man, But very unhealthy

(B)- Imagine you are a dog in a rich man's house, But very healthy

(C)- Imagine you are a Poor man, But very healthy

(D)- Imagine you are a dog in a poor man's house, But very unhealthy

The rich man has an issue,He is unhealthy but the poor man is not.So the rich man is fortunate to have wealth but not so fortunate to have health.But the poor man was the exact opposite.

Now consider this

(A)- Imagine you are a rich man, But very stupid

(B)- Imagine you are a dog in a rich man's house

(C)- Imagine you are a Poor man, But very wise

(D)- Imagine you are a dog in a poor man's house

As you can see even though one man is rich he has very low potential to reach nirvana.But the poor man is wise so he is with great potential.This change everything making him the most fortunate,the best birth among these four.

Now consider this

(A)- A god.

(B)- A human.

(C)- An animal.

An animal has no potential towards nirvana.But a man has much,therefore he is more fortunate and his life is good compared to the animals life.

But when you compare a god with a human you see that the god has much more potential than a human.So in this pair the god is the lucky one.

A good Karma

A good karma is something you do which would effect positively in this life or many lives to come.These could give you a birth with much potential to reach nirvana and make you healthy,strong,kind,wise and etc.It could also be powerful enough to give you a birth in higher realms,making it easier for you to reach nirvana.

So any karma that would ease your path to nirvana is a good karma,any birth that would give you a better chance to reach your path to nirvana is a good life / birth.

May triple gems bless you!

If your very happy, your very wealthy. Good karma could lead to a rebirth were one is poor but happy due to wholesome conduct in the present life like not clinging to the sensual or material world. Bad Karma could lead to a rebirth where one is rich but miserable due to craving the material or sensual world in the present life.

Karma doesn't have or reflect an agenda, so it's not agreeing with or encouraging behavior any more than the law of gravity is "punishing" someone who steps off a cliff by smashing them into the ground. But it still hurts or kills us if we step off a cliff - even if we do so mistakenly thinking we can fly. Gravity won't stop and go: "hmm, this is a perfectly nice person who is just confused and not suicidal, I think I'll let him/her down gently this time."

A major difference between karma and rules like the law of gravity is that karma is cause-and-effect of the mind, not just the body. Because we have minds, we can be happy and we can suffer. Each of us wants to be happy, so karma is called "good" when it brings about happiness. None of us want to suffer, and we call karma "bad" when it brings suffering.

However, we're just sentient beings so we are very confused about things most of the time, including about what intentions and actions will really bring happiness and end suffering. (All too often, we're the well-intentioned fool stepping off a cliff and meaning to fly.) The ethical teachings we study and practice in Buddhism are trying to guide us out of this confusion, as we train in more skillful kinds of behavior and thought. Most importantly, they call for long-term thinking: yes, being rich (if it makes you happy) is the fruit of good karma; but what use is it to build up good karma and then burn up the ensuing good fortune in mundane pursuits? On the other hand, if we adopt a vast motivation (such as bodhichitta) and aim toward awakening as a Buddha for the sake of ourselves and all sentient beings, all the acts of body and mind directed toward this end will eventually lead to stainless, perfect happiness of a different nature, one entirely beyond the stimulus-driven ups and downs of karma.