I think a related problem that each race is given a creator deity and that creator deity has a set alignment. Gruumsh the creator of orcs is evil. Lolth the corruptor of the drow was evil. Whereas Corellon and Moradin, creators of elves and dwarves, are good. In fact, most of the elf and dwarf gods were CG/LG respectively. Races matched the alignment of there race, and vice versa.
You're only going to break that chain by either removing racial creator deities (no gods of elves, orcs or dragons) or removing racial gods' alignments. You can still have a goddess like Lolth who corrupted a section of drow, but she didn't create the drow. Personally, I'd be fine with something like the Dawn War/Exandria pantheon but even more generic or something like Eberron where there are no racial deities at all.