It doesn't bother me at all. People on air usually have to talk a long time. Why do they have to live by someone else's standards? If their boss says it's ok to have a mug of water there, why is it our place to complain? I've never seen someone on air be rude or obnoxious about taking a drink. A little tolerance and empathy would be nice.
I am retired but work parttime in customer service at a midwest grocery store chain. We aren't supposed to have water with us and it's miserable after a couple of hours. We talk to customers all the time and move around a lot helping them with various things. We end up taking turns leaving our post to go get a drink.