Why are barbers closed on mondays?

I once asked a hairdresser about this. He told me that the custom of
barber shops closing on Monday dated back to earlier times, when
almost all barbers were members of a trade union. Since Saturday is
the busiest day of the week for barbers, they don't take Saturday off.
By taking Monday, they can get a two-day weekend (Sunday and Monday).
Union rules required this, and although not all barbers today are
union members, the tradition continues.

I can't be certain this is true, but it makes sense to me.

Throughout history many stores and service oriented stores have been
closed on Sunday.  Theory being they're open on Saturday and Sunday,
and Monday is the day off.  This goes way way back to ancient times.