Short story about annoying aliens going door-to-door to promote a religion

Question

Golden-age short story starts with a guy shutting his door on an inoffensive but boring alien going door-to door promoting his alien god. They are all over Earth, and bother people several times every day knocking on their front door, mouthing their bland patter, and handing out pamphlets.

Some dialog between the guy and his neighbor about how annoying this all is, and how daily life has degraded since the aliens came. Someone comes up with a stratagem that finally makes the aliens stop, or leave Earth, or whatever. Much celebration.

Closing scene of the story is the arrival of a brand new alien race in a threatening-looking spaceship burning across the skies, broadcasting, "Bow down before the flaming scimitar of [our own god]."

Edit: To answer a couple of the questions:

I can only tell you I read this story sometime in the '60s, possibly the '70s. I have no idea how old it was when I read it. I devoured anthologies during that period, so it could have been in any of those.

The "flaming scimitar" wasn't a quote, I just remember the original line conveying much truculence. The context of the story made it clear between the lines that the first aliens were meant to approximate Mormons or Jehovah's Witnesses, and the second aliens were meant to approximate Muslims.

Answer 1

It's Greg Benford's "Proselytes", which appeared in Full Spectrum (Lou Aronica & Shawna McCarthy, eds.), 1988. It was evidently also reprinted in his Matter's End collection. The plot matches the description given in essentially all particulars, even to the explicit contrast between "Mormon"-like and "Muslim"-like proselytizers.

The story opens with a visitation:

It was the third time something had knocked on the door that evening. Slow, ponderous thuds. Dad answered it, even though he knew what would be standing there.

The Gack was seven feet tall and burly, as were all Gacks.

"Good evening," it said. "I bring you glorious word from the stars!"

The conversation was among Junior, his Dad and his Mom, no neighbours, and they don't solve the problem; Dad just slams the door in the face of the latest Gack:

The Gack was still looking expectantly at them, waiting for them to convert to his One Galactic Faith. One of its four oddly shaped hands held forth crudely printed pamphlets.

"Now, now," Mom said. "We shouldn't make fun of another creature's beliefs. The poor thing is just doing what our Mormons and Jehovah's Witnesses do. You wouldn't laugh at them, would you?"

Dad could hold it no longer. The night air was cold and he was getting chilly, standing there. "No, thanks!" he said loudly, and slammed the door.

The Gacks don't leave, they are all destroyed by the new aliens:

When they went outside, the night sky was alive with darting ships and lurid orange explosions.

Junior cried, "The Gack ships! See, they're all blown up!"

But the ending of the story is a dead match:

Behind the swift craft huge letters of gauzy blue unfurled across the upper atmosphere. The phosphorescent words loomed with hard, clear purpose.

GREET THE CLEANSING BLADE OF THE ONE ETERNAL TRUTH!

"Huh?" Junior frowned.

Dad's face went white.

"We thought the Mormons were bad," he said grimly, "Whoever thought there might be Moslems?"