A whining differential is not a hazard. People have driven tens of thousands of miles on them. Even when you change the fluid, it might not go away. You can try a higher viscosity fluid, like straight 90 to help with the whine.
The only other option is to find a junkyard diff, and hope to God that it doesn't whine also. I don't know of anyone making these or even remanufacturing them.

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