My church doesn't allow food or beverages in the sanctuary, apart from water. The rule is there to keep the floors/seats/carpets clean.
If coffee was allowed, I'd probably have one. I don't see the big deal. Drinking coffee while listening to the sermon helps me focus: having to hold a hot cup of coffee upright requires just enough mental overhead to keep me from being distracted, or nodding off if I'm tired.
If people took advantage of the rule to bring in sticky, greasy, noisy, or smelly foods, that would be a distraction to others, and a maintenance nightmare. You can imagine what the floors and seats would be like if someone spilled a Coke--and how are you supposed to deal with that mess in between services? (Of course, you could say the same thing about coffee.)
Now, Piper is talking about appropriate activity during worship, not cleanliness. I personally fall on the "beverages are no big deal" side. It doesn't distract me from the matter at hand, and neither does someone else's coffee nearby. The thing I find funny is that Piper is simply
asking a question about the boundaries of liberty in worship--and, typically, the reaction he gets from the terminally online is to take great umbrage, like he's confiscating travel mugs at the door.