My immediate thought -- If they're using bluetooth and not the phone itself, they can do shit like put in external scanners for this shit at stores, stop lights, et cetera, and thus would know whomever goes near something or wherever you go without your permission, and no way to opt out. Yeah, the theory is, pandemic only, but the Patriot Act was supposed to be terrorism only and has been used to target center-right conservatives for the crime of disagreeing with Mastercard, so you should probably expect this shit to be used by the feds, the police, and Google AdSense as soon as people forget about it.
Sensors are fun. A fed could walk into a group of Antifa and ping, suddenly he knows every single fucking black masked idiot attending, instantly, and not only that, they could then use the bluetooth PAN feature to know what other Antifa people they meet with afterwards, where they meet them (thanks to GPS), et cetera. Instantly creating a digital contact web. Heck, it wouldn't even have to be a Fed, they could leave it in the trunk of a car on the side of the street and ping ping ping, every single person that walks by, their phone ID grabbed with a timestamp. Combine that with a hidden camera to ID individuals, maybe do this repeatedly so you can narrow it down a bit...
Oh, did you use a burner phone like a good little commie blackshirt? Well, I bet you took your burner phone home, and brought it into PAN range of your real phone. Ping!
With both Apple and Google doing it that's 99.9% of the phone market in the US. You won't be allowed to opt out.
The only option is to prevent them from doing this in the first place, but they seem to be of the opinion that your civil rights don't matter anymore because just absolutely because.
Granted they supposedly have a similar tech that uses audio instead of bluetooth. Your phone listens for a high frequency sound and dials home if it hears it, so they can make a noise and find out who all is in say, a drug house they want to raid, or what have you.