That's an interesting view but the issue with that is depending on what beliefs an individual has their opinion on what is good or bad will vary whereas Islamic morality is quite clear and unchanging. The biggest sin in Islam is shirk. Can people who commit shirk everyday (such as Hindus) go to heaven? Can people who believe in god but reject Muhammad and his teachings go to heaven? Highly unlikely. Can someone who rejects Islam even be "good" in the first place? How many passages are there in the Quran detailing the arrogant and evil ways of mushrikeen and kuffar? Maybe you can say people who have never heard of Islam will be judged separately and may go to heaven. But those people who have heard the message and rejected it (majority of people in the Western world) have very slim chances.
We human were gifted with intellect, we're able to determinant whether something is good or not based on our understand of that certain thing. We all know killing a another human for no absolute reason is a bad thing, based on the fact that he was innocent and that he has not harmed you in no shape or form. We also know that giving a another person something they desperately need (like food, money and house) is something that is considered good (charity). In today's societies, morality has been heavily influenced by abrahamic religions. because of this, you will find a lot of societies sharing the same principle of morality as the islamic one. So in a way, they already got the message of islam and they're already acting upon it's moral values.
"The biggest sin in Islam is shirk. Can people who commit shirk everyday (such as Hindus) go to heaven?" If that certain person turns away from shirk and becomes a muslim, all of his sins will be removed and he will start a new (but allah knows best).
"Can people who believe in god but reject Muhammad and his teachings go to heaven? Highly unlikely." In my honest opinion, i don't think so since they're rejecting the message of islam.
"Can someone who rejects Islam even be "good" in the first place?" Yes, if they hold the same moral value as the islamic one. Just because you're not muslim, doesn't mean that you're automatically bad.
At the end of the day, this is all our opinions. It is allah that has the final saying in whether you will enter hellfire or paradise. In allah we trust, to allah we will return. He is the most merciful, and the most forgiving. He is also the only one that knows us better then ourselves. He knows our past, presence and all the possible futures that we could have chosen and the one which we chose.