During the run of 'Sliders', they visited at least one new dimension each week; sometimes an episode began with them just wrapping up their adventure on some world on which we got only a minimal sampling of the differences from their Earth Prime-Time (or our Earth Prime.) One alternate Toobworld was highly litigious; everybody was obsessed with filing lawsuits against each other. On another Earth, there as an Azure Bridge in San Francisco, not a Golden Gate Bridge.
There was a world on which women were the dominant gender and another where women freely grew facial hair.
On that world, it was manifested mostly as tufts of chin-fur. But that might have only been the fashion style of that year. From this picture it looks as though women grew mustaches as well.
If so, that means it would have affected all the women in that society, even those who had counterparts in Earth Prime-Time.
And that would have included Mrs. Emma Peel, talented amateur, as seen in 'The Avengers'.
This is not to say that 'The Avengers' is to be found only in another dimension; just that there would be a dimension in which Mrs. Peel had a mustache. And there would be still another, that previously mentioned Toobworld where women ruled, on which Mrs. Peel would be the top professional and John Steed would be the talented amateur.
(That world of female facial hair would also mean there wasn't much call for the bearded ladies in the circus....)