Is there any evidence of this sort of acceptance between African and Asian elephants (say, in zoos)? I wouldn't be surprised if that had been attempted, and they appear further removed from one another than mammoths and Asian elephants are.
There was a zoo crossbred elephant. I think Motty was its name. It didn’t survive long after birth. But it shows that African and Asian elephants will breed at least, which implies they’d probably raise a mismatched calf.
Asian and African elephants are both commonly carriers for a virus (different strains of EEHV) which is very deadly to elephant calves of the other species. They used to be housed together more often before zoologists figured this out.