Let me start off by saying I think the Mansion is fine as is. But I also think that the Mansion was fine as was in 1969 / 1971. It's probably been tinkered with more than any other attraction. So any further revisions are keeping with the spirit of the Mansion (ha ha).
Now, specifically regarding a multi-racial Haunted Mansion... it's quite possible that this could be... AWESOME. If ghosts and ghouls leaving creepy old crypts from all over the world have retired here, then where are the Indian, Chinese, Sudanese, Kenyan, Moroccan, Tibetan, Turkish, Columbian, Peruvian and Inuit ghosts? What, we've got one mummy?! Surely we could do better.
In a nut, the Mansion could be given a dose of Mystic Manor multi-culturalism.
Of course, this could go horribly wrong. It could become a house of haunted stereotypes. But if done carefully (I'd consult Joe Rhode - who would in turn consult experts from the various cultures) there's no reason why a couple of the graveyard band ghosts couldn't be sporting a turban and a fez, right? Why can't a few of the transforming portraits have some Mexican folk art, some Japanese watercolors, and why not some Nigerian sculptures down the hall while we're at it. Why couldn't Madam Leota's seance have a touch more voodoo (Heck she could even be known by another name – Calypso, if you'd like to further strengthen the PotC/HM canonical universe.)
I suppose this raises the spectre of 'when' the Mansion is supposed to take place. In DL, New Orleans Square has always felt like it was 1920's-1930's, based on the live jazz music. To assume that the HM story takes place around then, and that you, a person from the 1920's, are visiting a place roughly 50 years older... yeah, a mansion that started gathering ghosts in the 1870's could be multi-cultural.
But in WDW, when is the adventure supposed to take place? Revolutionary War era? Surely not with the clothing worn by the cast members. Was the building supposed to be built during Colonial America but the story takes place... eh, mid 1800's? It's already a little sketchy. Adding more 'immigrant ghosts' would make it further detached from Liberty Square... but it's not like the Tangled tower isn't doing that right now.
So there, I turn this over to you. It could be great if done with vision and a budget. But I'm not sure if that's at all likely right now...