A story that is told in the first person by an obvious disabled and discharged military man, is definitely dystopian; I found it repulsive and gruesome.
It's "Ecce Femina!" by Bruce McAllister.
I'd guess it dates from the late 60's, or maybe 70's.
1972
Its beginning describes a lot of post-apocalyptic handmade signs like Andrew remembers, like:
SEE ORGAN LA FEY ON SATURDAY!
A guy has been out of circulation for several years (military? prison?) and returns home to a city in a shambles.
The narrator is trying to walk to town with a badly injured leg. He ruminates that he would have re-enlisted indefinitely, if it were not for the injury. (And other post-apocalyptic circumstances.)
A rough, mean gang of women on variously described motorcycles (Harley models, Triumph, etc.) come by him.
He tries to get a job at "Jack's Station". Jack is also a rough gang type woman.
The notable part I remember is a girl gang, who like to whistle the tune of "I Wish I Was an Oscar Mayer Wiener", then laugh in a sinister manner. The protagonist never learns exactly what it means, but it's clearly not nice.
One woman has Oscar Meyer (the story spells it this way, perhaps deliberately different from the hot dog maker company) patches. There is a reference to them whistling the song:
As if on cue, all the riders whistled the Oscar Meyer whistle, raised their arms and brought them down karate-style toward their crotches.
Then they were wheeling away, guffawing, someone still waving the man's rifle.
It also incorporated elements of social reversal, as there were no male gangs providing menace, only women.
There are no men groups, or gangs, and only the narrator and another man mentioned that I remember.
It's violent. There are descriptions of them beating up a man named Oscar.
This is probably your story, WhatRoughBeast. I hope you still have access to your account and find this answer.