Ziad al-Bayati took over responsibility for the cemetery from his father. I did find a Forward article from 2004 that indicated that one of the last Iraqi Jews was involved in fixing up the cemetery which had been neglected for decades, and gravestones damaged during the Gulf War were rebuilt.
And yet even in this article there has to be some old fashioned Jew-hatred.
The writer interviews an Iraqi "researcher" Ahmed Jawad who says:
It is a sign of the spirit of tolerance of Muslims, who respect the lives and bodies of their offenders, while fanatical Jewish organizations attack Muslim cemeteries in Jerusalem's Old City and the cities of Palestine and even in the European continent, as in Germany and France.
Incidentally, the 2004 article notes:
Visitors to the Jewish cemetery in the turbulent Shia neighborhood of Sadr City, the scene of some of the most vicious fighting in recent weeks, have been stoned more than once by school children.