I scanned the names of the various authors, wondering which of them had become successful after being published in this anthology, then looked at the table of contents wondering if any of the titles would ring a bell. I recognized In the Barn by Piers Anthony immediately. It's a shocking tale of an investigator who visits an alternate reality Earth where animals couldn't survive. Humans are required to fulfill all the roles that animals fill in our world. Women are literally the cows in the barn. Hitch, the protagonist, is shocked down to his toes, but in the end wonders which world is a better, more moral, place for humans.
Although I did not become a vegetarian after reading that story (way back in 1972), it must have been churning around in my subconscious enough for me to eventually give up meat sometime in the early 90's. Yeah, yeah, I know, 20 years is a long gestation period. *snort*
I think I'll start looking for Dangerous Visions in some used book stores.