Though you have indicated this is a short story I believe this may be the Robin Cook 2000 novel Abduction.
Points that match:
I read this short story probably 5 to 10 years ago.
Partial check. The novel came out in 2000.
There is this utopian land where the people are basically immortal thanks to being able to transfer into a new body when they get old, or just sick of the body that they have.
Check. The Moho (a hidden human race living in the Mohorovičić Discontinuity and can transfer into clone bodies and are essentially immortal.
There's a wait time, though, to get a new body. If someone has to vacate their body, or wants a new one, their consciousness is uploaded into this central computer thing while they wait for the new body. You can visit them there in the central place to talk to them.
Check. Consciousness can be uploaded to a "master computer" location.
Wait times vary for new bodies and I remember the characters discussing the pros and cons of deciding to get a new body depending on the current wait time, and hoping that their next body has better knees, or less aches and pains, or problems or whatever.
Check. In some cases the choice is to accept a new body that is a child. Others wait until they are adult in form.
The society is hedonistic - they have endless cocktail parties and lots of sex - polyamory all around regardless of gender.
Check. The Moho population are genetically engineered, almost perfect humans. They are vey sexually open.
Somehow these outsiders enter this hedonistic utopia,
Partial check: "A team of researchers in a remote region of the Atlantic become trapped inside an ancient undersea volcano when their submersible is inexplicably drawn in." This is actually more than just two people though:
Dr. Suzanne Newell
these two(?) guys that are basically idiots.
Check. At least two of the guys are idiots that, without giving away too much of the plot, really make a mess of things.
The immortal people welcome them but the outsiders screw it up. One of the old men transfers his consciousness into the body of a young woman, and then ends up hitting on one of the outsiders.
Partial match. The Moho do not understand the repugnance some of the outsiders have for homesexuality. In an effort to "help" one of the Moho females seduces one of the outsiders. In a very casual manner during intimacy, she brings in an Moho male. The homophobic outsider male kills the young Moho woman and/or young Moho male and then tries to hide the body. I think inside a vase.
The outsider has a homophobic freak-out and murders the young woman, I think by hitting her over the head with a heavy vase or something. I think the outsiders try to hide the body, but they kinda screw that up too, and of course everyone finds out.
Check, check & check.
This murder is the first death that the society has known.
Virtual check. It is the first murder in hundreds (if not thousands) of years.
Anyways, trying to think of what this story is is driving me nuts. It's probably a short story that's fairly old, maybe 1950s-1980s, but maybe not. It's at least pre-2010. It probably wasn't very well written but for some reason it's stuck in my head now. Thank you in advance!
Because of the "Lost World/Pellucidar/Atlantis" type setting, the book does have the feel of a an older "pulp fiction" type book. I kept thinking of the Pellucidar books by ERB when I was reading it. Too, I would have to say IMHO it is not one of Robin Cook's better novels.
If this is the story of which you are thinking, you may remember the twist ending:
Fearing for their own safety and the discovery of their civilization, the Moho-dwellers feel they cannot allow their abductees to return to the surface. The research team manages to recover its submersible and mounts an attempt to return to the surface. However, at the last moment they encounter a large Moho craft and emerge to the ocean's surface in the late 18th century. The group abruptly discovers that the craft was actually some sort of advanced Moho time machine and/or spacecraft that sent them 200 years into the past to prevent them from alerting the surface world to the presence of the Moho-dwellers.