No matter what your feelings are about the fanny pack, the fanny pack can arguably be considered a personal item or personal attire.
The official answer is the fanny pack is considered a personal item (at least according to Frontier and Delta), but usually, it is not. Most flight attendants won't care about enforcing it, unless you're traveling on a very strict airline.
By the way, this axiom holds true across most travel policies, including those regarding carry-on size limits and the makeup-liquid debate:1 It's only a problem if the person you're encountering deems it as a problem.
The chances of that are usually low.
On the last few flights we wore the fanny pack, we were waved through security and the gate just fine (through Delta via JFK and BER). This applied to all of the both domestic and international trips we have taken so far.
For the risk averse, there's this solution: Wear the fanny pack onboard, and make sure there is some space in your personal item bag in case a few airline staff members get upset. Easy!
