IN our family, there are two kinds of situation and they are completely distinct. On the one hand, there is no way I would think it was ok for anyone to come to the dinner table and read an online blog or newspaper or Mumsnet or Reddit etc systematically. It's never even been discussed as anything but normal that we discuss, normally. (This is dinner, btw. Breakfast, only fiends interact. Go read your online newspaper by all means, leave me alone until I've had my coffee/tea/toast!)
The second situation at dinner is that someone has to look something up: we're always a bit apologetic, but parent mentions that they need to be out such-and-such day, is that ok, and other parent, plus possibly child, needs to check their calendar, which obviously (!) these days is on their device. Or someone avers, in the course of an active if not necessarily (!) peaceable conversation, that this or that fact is true, ie say Boris Johnson was blamed by the commission or Palestine already had so many Jewish residents in year X or it was Charles Dickens who coined the line (can you tell it's exam season? and that we're all avid news readers) and we have to have someone go check and show us all on screen. In other words, if you're using your phone as a dictionary/encyclopedia/calendar, fine. One-off.
The only other situation has literally been: you are waiting for a call from your relative's doctor/other crisis. Allowed to check caller ID, but if it's a random from some friend trying to reschedule lunch next week, check and let it go to voicemail.