I think it's because the barbers want a 2-day weekend too, and are usually open on Saturdays because that's when their customers have the time to come in.

Historically, many American cities had some sort of Barbers Union, often affiliated with the AFL. These Barbers Unions were part of a larger trade-union movement that lasted through the first half of the 20th century.

If you google "Barbers' Union Employers' Guild", you'll find a bunch of newspaper and magazine articles from that period.

I've heard anecdote that during the period of their greatest influence in the early-to-mid 20th, Barber's Unions placed pressure upon their employers for no-one to be open on Sundays or Mondays, so that the Barbers could have a proper 2-day weekend, and so that no one shop was at a competitive advantage by being open on a day when most others were closed.

A survey of the appearance of industry labor disputes in court records, and on the front page of newspapers, makes this anedote at least plausible.

There appears to have been both an Employers Guild and a Journeyman's Union related to the profession of Barbering in the early 20th century..

I confess I don't really understand the labor politics of the period well enough to attempt an explanation. However, several of our specialist flairs in labor history might be able to contribute further.