I'd also love to see deity choice being tied to domain choice and in some cases to race as well.
I have always seen religions as a social, rather than racial, construct. So if my dwarf cleric has grown up and trained a major dwarven settlement, she is likely yo follow one of the dwarven gods. If, however, she is born and raised in a human settlement, she might follow the religion of her parents or decide that one of the human gods better reflects her own worldview.
Just as you have Western people following Eastern religions in the real world, so the D&D religions should be open to any race.