The privacy issues come from the app, not the headphones. Don't use the app and you're fine.
General privacy rules apply: any data you provide will be stored and sold. If you tell an app your height, weight, etc, the company will sell that. That shouldn't be a surprise to anyone.
The only interesting bit here is Bluetooth tracking, meaning people can see a unique identifier by being near a Bluetooth device. This is true for all Bluetooth devices (and honestly any wireless protocol besides point to point wireless), so not unique to headphones. If your phone connects to cell towers, your headphones aren't going to be the ones breaking your cover...
Beacons don't track you. You track the beacons. That's why they're called beacons. The article is claiming beacons (or other bluetooth devices) could track you if your device was in pairing mode, which is not a real scenario.
They don't just transmit it while in use though. I guess someone could track where you were each time you paired it but as you said cell towers already track you all the time