Seems to me that some races, Warforged come to mind, almost necessitate separate backgrounds, or at least highly refluffed.
I don't see why?
Acolyte: served the temple of Silver Flame on constant vigil and in prayer so that no matter the hour a worshiper would find a comforting individual to talk to, even when the other were asleep or away
Charlatan: helped con other warforged with your dwarf friend out of spoils of war after the Last War, selling "repair oil" and "components" that would help them find a new purpose or calling
Criminal: refuges are easy marks and a warforged has to eat, well he doesn't but it is so much easier to send gold to Lord of Blades when you just take it from insignificant lesser races
-Spy: the Black Lanterns always need a good loyal agent that can hire on as just another jobless warforged bodyguard
Entertainer: never saw the war a noble kept you as a jester for his son after watching you trip falling into formation on your first day of coming to the castle, the child hadn't smiled in years now he is older and you bring joy to other children
-Gladiator: a room another sack of flesh to kill on the cold stone floor and then back to your box, you stoped counting the dead, you stopped talking, you stopped living, until she set you free now you serve at her side keeping her safe only killing if some foolish piece of meat tries to kill her
Folk Hero: you were on a delivery mission when the Karnathi soldiers and undead attacked the small town you were in, you did the only thing you could do and stood with the few men folk left, thanks to you many lives were saved that day, they didn't have to build a statue of you in the center of town but it does give you pride.
Guild Artisan: House Cannith, you helped make more like yourself you gave life to other warforged something you are very proud of.
-Guild Merchant : Cannith needed a demo model and that was you
Hermit: war, so much death, some call you a deserter, you try not to think of it, not another life will be lost by your hands ever, only by study of medicine can you help to undue some of the hurt you brought to the world
Noble: Your mother was as they say touched in the head, for you know she isn't your mother, but don't ever let her know that. Her real son died in the war, so did her husband, her brother, and her father. When you escorted the officer to deliver the news she took possession of you and has treated you as child ever sense.
-Knight: trained as a squire for the last five years of the war, the eve before the Mourning you were made knight by Sir Hendrix on his death bed. Now you try to give other warforged a shining example to look up to so they are not tempted by your sworn enemy the Lord of Blades.
Outlander: After falling off the side of that airship and spending years in the wilds, you made some use of your skills leading refuges through the mountain passes
Sage: The giants of Xen'drik hold the key in the history, sent as an aid to a professor from Morgrave University you have spent most of your existence trying to find the lost pieces of the puzzle.
Sailor: House Lyrandar is a good employer you spent the entirety of the last war being the boatswain on a war vessel
-Pirate: after the war the crew mutinied and went pirate
Soldier: well duhh
Urchin: you awoke on the lower streets of Sharn, no memories, no money, no name, taken in by some of the locals they mention things like the Last War and this means nothing to you, apparently making new warforged is a crime but you think that is what you are no nicks or scratches on your body and nothing before that moment you awoke in your head