Without being snippy, the idea that drinking a cup of coffee whilst you talk to people is 'unprofessional' comes (IMO) from people who think professionalism consists in wearing a suit and looking important.
If you are an intelligent person with a good head on, that comes across. Whether or not you happen to consume a cup of tea during the morning of your interview will really not affect that. 
Also, in quite a lot of places, 'fit with the team' is an important part of the interview. Frankly, where I work, if someone was so up themselves that they wouldn't have a cup of tea during the breaks, that would be a bit of a red flag. We might spend 20 years having day-long meetings and away days with this person.
And surely interviews are quite long, mostly? At least, I am an academic and interviews are minimum 6ish hours long, IME, and sometimes over 2 days. I have been flown to a foreign country for 3 days for an interview once; also another time, had to go out for dinner with the panel the night before the interview. Having lunch as a group is quite normal, also tea and coffee--as the interview will normally consist of multiple presentations/ interviews/ etc. It would be inhuman not to offer refreshments during that!