Not sure about grease making the oil milky, but water definately will. Check where your breather is, and possibly extend it for future assurance. Heard from a local 'diff-repair specialist' that when diffs are hot they can suck in water from 'other' places/seals etc...stand to correction on this, but believable as I had the same problem.
Drain the diff. Refill with whatever oil you're using (normally EP90). Then check again once you've driven...if still a bit milky, then repeat the process - until the oil is normal colour.
M2CW, hope that helps.
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