Most of us have seen images from e.g. President Kennedy's funeral and Princess Diana's. Being photographed is an extra and most probably unwelcome strain for those attending the funeral for a member of the public, but those that want it would let people know. The funeral following my uncle's at a crematorium had people all brightly dressed, so they must've known was expected.
As I live in a village of less than 500, it's almost expected that I should attend (off duty) any local funeral, so it's a more regular type of event for me than if I lived more anonymously in a large community. I may attend half-a-dozen funerals a year while others of you may not have been to that many in your lifetimes.
A funeral in the summer was for a teenager who'd died accidentally. The county newspaper had a photographer there for the arrival of the coffin. Though many were aware of his presence, it only caused a few comments among those in the church. I recorded the eulogies but was asked by the mother of one of the friends who'd been with the lad if I'd managed to take any photos. Later that day I went along to photograph the floral tributes and met the family at the grave. The lad's younger siblings asked to have their photo taken, which must be one of the most poignant shots I've taken, with the parents kneeling in the background, tending to the tributes.
Based on the hassle involved when photos are taken in the same village at events with children involved, I wouldn't relish the opportunity unless everyone was forewarned. In the surrounding towns, where I'm less well-known, people may be less likely to interrupt what I was doing to express their opinions.
A New Orleans or other "performance style" funeral should be a great job to get, and the photographer featured in the article is probably dealing with families with less of the "British reserve".