I think you just go back to their roots, and just turn them away from being always evil. It's really not that strange of a result. Originally, orcs were the enemy because they were
chaotic. Chaotic in the sense that they have a distaste for Law. In particular, the human form of civilization.
First, note that we're just defining generic orcs. Much like generic elves and generic dwarves, orcs need a generic flavor. Any campaign can change that, but the MM needs to define them, too.
Orcs in D&D are human-sized green-skinned humanoids that tend to live in nations, tribes, or clans in the wilderness. Like elves, they prefer nature, and want the world to be covered in forests and wildernesses teeming with life. They generally oppose the kind of organized civilization that humans bring. They see little value in building permanent walled cities, building cultivated fields for farmland, roads, etc. Humans invade a region and tame it to their will. Orcs are much more interested in being the alpha predators of their region, and living with what is there instead of changing it to suit them. Orcs hunt wild game, fish in rivers and lakes, tend groves of wild vegetables, and are famed for producing some of the strongest and most intoxicating liquors and wines. They often hold celebrations that feature games of athleticism or acrobatics or martial skill. Orc martial prowess is legendary in most parts of the world, with some of the greatest swordmasters known being orcs.
Most orcs will band together to face a common threat, making orcs powerful allies and deadly foes. Orcish hordes and war bands are legendary for their ferocity and tenacity, and many an army has fled the field before facing a charge from orcs. Some orcs are more hateful than their brethren, and reject the notions of peaceful existence, instead adopting the bloodthirstly ways of Gruumsh, an old, evil god of the orcs with a particular dislike for humans, elves, and dwarves. These "lost" or "dark" orcs may form war bands or hordes intent on looting cities and towns or killing other creatures they see as harming or invading the lands the orcs call home. Most orcs find such behavior distasteful, and reject the teachings of Gruumsh as self-defeating and pointlessly destructive. Unfortunately, because most orcs are disinclined to visit the cities of other races, the memory of these war bands has left a poor impression of orcs on many human nations.
As a people, orcs are known for being passionate, proud, athletic, brave, and willing to act decisively and promptly. Orcs may also be brash, arrogant, or short-sighted. They are fiercely loyal to their clan, family, or code, whether that's their own by birth or an adoptive one. They are also known for being unwilling to let go of a grudge, an unfortunate failing they share with both elves and dwarves. In some areas orc feuds with elves or dwarves have lasted centuries, long past when even their longer-lived neighbors can remember the cause. Play an orc if you want to be quick to laugh, good in a fight, and a strong and loyal friend.
In following with their Orcs tend to be chaotic, much like elves. They live much shorter lives, of course, and so they are not patient or aloof in the ways elves are. Most Orcish settlements tend to appear smaller and blend in with their surroundings. Orc settlements are also often semi-permanent, as they may migrate or travel throughout the year to find better hunting. Though in war they are known for building large forest fortresses and palisades for protection when necessary, orcs like to use the natural geography to protect themselves.