Hi @MxxCon - good question. In this case, I was just syncing up a few errors with the status quo of the rest of the cemetery, but I was wondering the same thing. 

For several ones I've checked out in person, there are "Private" and "No Trespassing" signs at the entrances, but they do seem to function more like "permissive" since nobody checks you in or asks. I referred back to the OSM wiki, which seems to prefer legal access over practical access making me think these should be "Private." I usually traverse these areas by bike, and some (like Green Wood Cemetery in Brooklyn) will actively stop you and make you park your bike to enter, whereas at Mount Olivet in Queens I didn't have that experience. 

What do you think is the right designation?