Thanks for being a nice neighbor.
Avoid anything alcoholic and all kind of meat except seafood. If it has to be food consider fruits or dried fruits (dates, almond, nuts…), honey and olive oil are also among guifts we give in my area (Morocco). A nice box of dates is my favorite or a game/toy for their toddler/child if they have any.
Can’t you be frank about it? like “sorry dude, nothing personal but I just want to mind my own business while having my hair done”, a little “thank you for respecting that” at the end with slightly extra tip and you will both become your favorite barber/client.