If you don't understand that a goblin sees himself as the hero of his own stories, I don't know what to tell you. Moral ambiguity exists in D&D. The fact the entire game is built around killing and looting is a prime example of the moral ambiguity of the game.
If a party of Good characters is based around killing and looting, then I think they have ceased to be Good characters. More commonly, I see them undertaking missions requiring them to kill the enemy for the greater good, and spoils of war come along with that. A slightly different description for the same thing, but if they just wander aimlessly looking for somewhere to wreak havoc, they are not "good" characters.
Or are you one of those DMs that forces paladins to save orc and goblin babies after they wipe their parents out? Or hill giant children on the chance they can be redeemed?
Is it OK to slaughter helpless infants? Is it Good? By the book, Good people make sacrifices to help others. "I can't be bothered to deal with these babies so put them to the sword" seems less than consistent with that ideal. But I also ask "are you one of those DM's who assumes that the orc, goblin and hill giant babies are innately evil, so even if raised by kind, loving surrogate parents to follow the ideals of Law and Good, they will always revert to evil because they are orcs, goblins and hill giants, and orcs, goblins and hill giants are just naturally evil?"
If so, I suggest you have established that these creatures are like demons and devils - paragons of their baseline alignment, and beyond any hope of redemption or saving. In that case, "put them to the sword" seems the only reasonable answer. If, however, we accept that these beings have moral choice, then perhaps the heroic characters who make sacrifices to allow these beings to have a chance at redemption ought to be rewarded with seeing their efforts bear fruit in the form of adult Orcs, Goblins and Hill Giants who follow the tenets by which they were raised, and perhaps even convert others of their kind to a more peaceful path.
Or we can just have a dungeon crawl where we hack and slash, but nothing on a broader basis is ever really changed, much less improved, as a consequence of the characters' actions.
Or don't allow slavery in Lawful Good societies because you have a modern day view of slavery as something vile rather than the view of people that didn't have a lot of resources for prisons and thus enslaved other groups as a means of penance for aggression and a show of mercy?
If the slaves are treated in a manner consistent with the ideals of Law and Good, I could see such slavery existing in a Lawful and Good culture, just as I could see such a culture executing the perpetrators of certain heinous crimes. They would not condone mistreatment of slaves, and just as they regret the need for executions, would regret the need for enslavement or imprisonment. "Love the sinner, hate the sin".
Good people protect innocent life, but still mainly do so for their own kind just as real humans. Goblins might very well view themselves as innocent victims of evil adventurers who show up at their doorstep, kill their people, and take their stuff.
And, if those adventurers just go off without provocation slaughtering goblins who have done no harm, perhaps the Goblins are good and the Humans evil.
So when you discuss doing so "for their own kind", how far to we take that? Can the Humans raid elvish encampments, kill their menfolk and sell their women and children into slavery, and be Paladins maintaining their Lawful Good alignment? If we change Elvish into whatever human nation ours may border, do the same rules apply?
Humanity has never had to contend with multiple sentient species, so we have no real philosophy for dealing with the issue. Does "do unto others" apply only to:
- my blood relatives? [pretty narrow scope]
- those who live in my village?
- those who live in my nation?
- those who have the same skin colour?
- those who are the same species?
- player character races?
- all sentient beings capable of moral choice? [pretty broad scope]