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Isn't that kind of where the phrase "Keeping up with the Joneses" came from? I've never read anything like that in the Hugo Award winners anthology I picked up at a garage sale last month, and that book had "I Have no Mouth and I Must Scream" in it. Maybe you could check the websites for Analog or Asimov's Science Fact and Fiction.
So far no luck with this one. Searching through archives of short stories has so far increased my "to read" list but not turned up the story I'm looking for.
Mom says that in the same anthology is a story about a man who, while at a comedy club, realizes he's the last intelligent man (which is a lousy search string).
Where there's life, there's hope.
"Sources of The Nile" (Avram Davidson) was suggested on Library Thing and that MIGHT be it. Waiting for a copy of the book now.
Powered up in 1971. Brought online in 1982.

This is a short story about a family who are mocked/made fun of/thought to be weird because of the things they do/like/wear/etc.
After a time, tired of the teasing, they move away and everything that they did and were mocked for becomes popular. Of course, by that point, the family is into new things. Essentially, the family is just slightly ahead of everyone else as far as trends go.
It’s speculative fiction, but might have been marketed as science fiction or fantasy. It was very likely written and/or published in the late 1950s or during the 1960s. I could be completely wrong about the dates. My mom remembers reading it in an anthology, but can't remember if it was a "year's best" collection, a collection of one author's short stories, or even if it was just in a sci-fi/fantasy magazine.