"At the Conglomeroid Cocktail Party", a short story by Robert Silverberg. It first appeared in the August 1982 issue of Playboy, not Omni.
It is in a time when humans can have any form they wish. It starts with a party of transhumans who invite their guests to pick a form for their child to be.
So when quasi-cousin Spinifex called and said, "Come to my fetus-party tonight," I accepted unhesitatingly. Spinifex lives in Wongamoola on the slopes of Dandenonga, looking across into Melbourne. I happened to be in Gondar on my way to Lalibela when his call came. "Mortissa and I have a new embryo," said Spinifex. "We want everyone to help us engineer it. There'll be a contest for the best design. The whole crowd's coming, and some new people."
And the shock of the party is that a woman submits a normal human form and it is considered rave, very cool — but not used.
She took the podium, grasped the stick, closed her eyes, sent her thought-projection to the screen with an intensity of effort that turned her fiery mantle bright yellow and sent it arching out to expose her blue-black furry nakedness.
On the screen a standard human form appeared.
Not quite standard, for it was hermaphrodite, round rose-nippled breasts above and male genitals below. Yet it was the old basic body other than that, the traditional pre-Shaping shape, used now only by the unfortunate billions of the serving classes. I gasped, and I was not alone. It's no easy thing to amaze a group so worldly as we, but we were transfixed with amazement, dumbfounded by Domitilla's bizarre notion.
And it has to do with a male transhuman who becomes obsessed with this very hip woman-creature who would dare submit a human form. He is shocked and dismayed, heart-broken when she goes to Kathmandu and takes on this base human form.
"I beg you—stay as you are a little longer."
"I undergo engineering tomorrow at dawn," she said, "at the gene-surgery in Katmandu."
[. . . .]
The inner door opened and nurses came out, standard humans, and an orderly or two and then the surgeon and then Domitilla. I recognized her at once, the same wiry armature as ever. The new body she wore was the one she had designed for the child of Spinifex and Mortissa. A standard human frame, mortifyingly human, the body of a servant, of a hewer of wood and drawer of water, except that it glowed with the inner fire that burned in Domitilla and that no member of the lower orders could conceivably have. And she was different from the standards in another way, for she was naked, and she had used the hermaphrodite design, breasts above, male organs below. I felt as if I had been kicked; I wanted to clutch my gut and double over. Her eyes gleamed.
He gets over it until this wasp-combination laughs at him at a party — and he knows it is her.
"Look over there," said Melanoleum.
I followed her glance, past Hapshash and Mandragora and Negresca, to the slender, taut-bodied stranger scooping fish from the pond: beetle-wings, black and yellow, luminescent spots glowing on thighs and forearms, cat-whiskers, needle-sharp fangs. She looked toward me and our eyes met, a contact that seared me, and she laughed and her laughter shriveled me with post-causal mockery, contra-linear scorn. In front of them all she destroyed me. I fled. I am fleeing still. I may flee her forever.