We have an old cemetery in town that was torn out in the 1940's, turned into a park and subsequently a schoolyard. There's an athletic field, tennis courts, playgrounds and a running path through it. I've hunted it many times and the passersby are always interested in what I'm getting out of there. Never had anyone complain.
Did have a fella tell me he was part of the team that excavated for the gymnasium and approximately 12 bodies came out during that work, graves that had not been moved, though they were reported as such. That dirt with those bones went into backfill the site of another school in the district, so the story goes.
I've also turned a bucket or two of old casket handles over to the local historical society.
As to whether or not it's a good place to hunt, I've found lots of silver there, many IH's, some jewelry, old and new toys, and bones. (ham, steak and chicken especially) as many people had post-funeral picnics in the same park back in the day. Also found one bottle dump with very old local beer bottles in it at the site.
No, I wouldn't hunt an active cemetery, that includes any long-forgotten place that still holds headstones or markers or is known as a cemetery.