"Puppet Show" by Fredric Brown
Horror came to Cherrybell mounted on a burro led by an ancient, dirty and gray bearded desert rat of a prospector who later—nobody got around to asking his name for a while—gave the name of Dade Grant. Horror’s name was Garth. He was approximately nine feet tall but so thin, almost a stick-man, that he could not have weighed over a hundred pounds. Old Dade’s burro carried him easily, despite the fact that his feet dragged in the sand on either side. Being dragged through the sand for, as it later turned out, well over five miles hadn’t caused the slightest wear on the shoes—more like buskins, they were—which constituted all that he wore except for a pair of what could have been swimming trunks, in robin’s-egg blue. But it wasn’t his dimensions that made him horrible to look upon; it was his skin. It looked red, raw. It looked as though he had been skinned alive, and the skin replaced upside down, raw side out. His skull, his face, were equally narrow or elongated; otherwise in every visible way he appeared human—or at least humanoid. Unless you counted such little things as the fact that his hair was a robin’s-egg blue to match his trunks, as were his eyes and his boots. Blood red and light blue.
....
Dade Grant was peeling off his beard and wig. He rubbed a cloth across his face to remove makeup and was revealed as a handsome young man. He said, “what he told you, or what you were told through him, was true as far as it went. He is only a simulacrum, yes, but he is an exact duplicate of a member or one of the intelligent races of the galaxy, the one toward whom you would be disposed—if you were violently and incurably xenophobic—to be most horrified by, according to our psychologists. But we did not bring a real member of his species to make first contact because they have a phobia of their own, agoraphobia—fear of space. They are highly civilized and members in good standing of the federation, but they never leave their own planet.
“Our observers assure us you don’t have that phobia. But they were unable to judge in advance the degree of your xenophobia and the only way to test it was to bring along something in lieu of someone to test it against, and presumably to let him make the initial contact.”
The colonel sighed audibly. “I can’t say this doesn’t relieve me in one way. We could get along with humanoids, yes, and will when we have to. But I’ll admit it’s a relief to hear that the master race of the galaxy is, after all, human instead of only humanoid. What is the second test?”
“You are undergoing it now. Call me—” He snapped his fingers.
“What’s the name of Bergen’s second-string puppet, after Charlie McCarthy?”
The colonel hesitated, but the tech sergeant supplied the answer, “Mortimer Snerd.”
“Right. So call me Mortimer Snerd, and now I think it is time that I—” He lay back flat on the sand and closed his eyes just as the stick-man had done a few minutes before.
The burro raised its head and put it into the circle over the shoulder of the tech sergeant. “That takes care of the puppets, Colonel,” it said. “And now what’s this bit about it being important that the master race be human or at least humanoid? What is a master race?”
Someone asked about it here on Reddit. Found with a search query for science fiction story man alien "donkey"
