For merchants, Cash > Credit, cuz they don't have to pay fees to the cc companies. The places that do except credit, only do so because they don't want risk losing customers to there competitors.
Barbers are amongst one of the few businesses left where most people expect to have to pay cash and will do so. However, there's a limit to what most people will spend with cash. Since most keep raising their prices coupled with the fact that many cheap fast food places now take cards means that they're going to have to start taking cards.
One potential issue is that many barbers rent their chair, so a centralized system for the shop may prove cumbersome. However, thanks to technology, there are systems being developed where people would be able to except cards on their smartphones, thus alleviating this issue.
This could prove especially beneficial if you're the only barber in the shop who takes cards.