This is "Battlefield" by Harlan Ellison; first published as "His First Day at War" in the November 1958 issue of Space Travel. Previously identified as the answer to this question.
The dinner party is just a small part of the story, which begins on the moon. Here is some dinner conversation:
Then the forks went into the food, and mouths opened, and dinner was underway. As they sat and discussed what was what, and who had gotten his, and wasn't it wonderful how the moon was the battlefield, while the Earth was saved from more destruction like those 20th Century barbarians had dealt it.
"Listen, Bill," Massaro jabbed the fork into the air, punctuating his words, "next Sunday you and Yo and the kids come on over to our hovel. It'll cost you for a robo-sitter next week. We're sick of laying out the credits."
They smiled and nodded and the dinner date for next Sunday was firmed up.
Back to work on Monday:
The commuter platforms. The ships racked one past another, pointed toward the faint light they could not see. The light of the dead battlefield. Moon. The Blacks in their regal uniforms queueing up to enter the vessels, the Whites in splendid array, about to board ship.
A Black ship lay beside a White ship.
Bill Donnough boarded one as he caught a glance at the ship beside. Massaro was in line there.
"Go to hell, you White bastard!" he yelled. There was no friendliness there. No camaraderie.
"Die, you slob-creepin' Black! Drop!" he was answered.
Later that evening, Bill Donnough would start looking for another home to attend, the following Sunday.
Who said war was hell? It had been a good day on the line.