I feel kind of ok with it if there are main cement trails going through it... but it can feel a bit awkward if you see people who are there to pay their respects.
There's an orienteering map in Montreal where I have run a course where you had to find answers to questions on tombstones... huge cemetery with park around, so maybe thats more ok?
Canada's multiple (more than 80!) world record holder, 85-year-old Ed Whitlock, famously does all his training in a Toronto cemetery. He is the only person ever to have run a marathon under 3 hours over the age of 70 - 2:54 - so he's done some long runs around that short loop. He says he feels safer from cars in a big city and it's shady on hot days - also, he probably has some friends in there so it may seem more welcoming than an unfamiliar cemetery. This article is 2 months out of date; he just set an 85-89 world record for the mile last week.
Back in the days when my phone number was the listed one for climate enquiries at the Bureau of Meteorology, I took half a dozen phone calls in the space of a day from someone who was convinced that the world was going to end on 6/6/06 and that it was our responsibility to warn the Australian people about this. I marked the occasion by leading our club training run on a lap of the Warringal Cemetery.
May depend on the occasion. Normally, Arlington is off limits to runners. But the Army staff runs it in silent formation, no cadence, for the Army Birthday. I hate formation runs, but this one is by far the exception.
I like running through cemeteries (not jumping up & down on the graves, obviously) but often have difficulty in convincing my friends to join me. There's a large lawn cemetery near me which I think would make a great sprint map but somehow I don't see it happening...
I've done a fair amount of running through cemeteries but I think yesterday was the first time I'd done so when there were people there paying their respects. I felt a little weird doing so, though I think if they saw me they just ignored me. I have never visited a cemetery for purposes other than running, tourism, or geology field trips, so it's hard to think about it the other way around.
If there are live people there, maybe an issue, but the dead people don't mind. With that in mind, old cemeteries are fine, because there's nobody left alive who knew the dead people, so they aren't there crying about cousin Fred who died last week. There's a colonial era cemetery in my home town, and we used to go there and make rubbings of the tombstones when I was a kid, and it was fine (though some places have a prohibition on that). And running is a far cry from beer parties or sex or knocking stones over.
There's a cemetery in town here that's also a main way over the West Hills for cycling - everyone stays on paved roads, and it's usually just one or two people at a time. I don't think that's bad, and I don't think a single runner would be an issue either. Big group rides with chatting or a pack running and carrying on a discussion would be something different though.
I've also definitely run through the cemetery that's around the block from my house, and it's never seemed inappropriate. And there's hardly ever anyone there.
I feel like it should be fine on the paved roads, but I would understand if people there to pay their respects were upset at you blithely recreating in the cemetery. I'd avoid any funerals or other gatherings of people.
Last winter, an informal training run in our club had a few controls in a cemetery. There were definitely no flags, but maybe ribbons or nothing at all - I don't remember now. If I remember correctly, everything off paths was marked olive green on the map, so we did not run through the graves. It did feel a bit awkward, but, fortunately, there were no people except for the runners.