We're nearly at the "Foundation" levels of surveillance tech, but with no countermeasures in sight to oppose that. Even resisting web browser fingerprinting is difficult.
There are no "hard" countermeasures possible, not technological ones - you're fighting against the laws of physics here, which mandate that everything constantly radiates information about what it's doing, in every direction, at the speed of light. Advancement of surveillance is advancement in being able to discern that information. You can try and introduce noise, but you're still fighting uphill, against the whole fields of signal processing and information theory.
The only "countermeasures" we can have are "soft" ones - social, political and legal. Convince people to treat privacy as core value, and surveillance as repugnant. Make forms of surveillance illegal. Mandate by law to have surveillance capabilities in devices handicapped by design. But this, at best, only solves the problem for regular people and some of the time, while governments stay stable and sane - the possibility of deeper surveillance is still there, just the choice to perform it seems unattractive at a given moment.
A Halloween costume that changes the shape of the body and face should suffice. Let's all dress up as "V" from V for Vendetta. Some would say a persons gait can give them away so we can all walk or sashay like a runway model. The costume needs an RF blocking pocket for fondle slabs. I can picture this happening. Low tech, affordable, concept can be applied to any costume. Optional platform boots to balance peoples height.
I think we still have an option of a privacy regulation that requires explicit expiring consent on any kind PII handling and a private right of action to enforce it (e.g. small claims court).
There are strong incentives for secrecy (military applications), hence encryption which provides solid foundations for private communication in civilian tech. I wonder if counter-surveillance tech could take the same route (e.g. ordinary soldiers can no longer afford to not carry a smartphone -> strong incentive to protect them from tracking; maybe I'm extrapolating too far).
It's more likely that the military would provide soldiers with phones using a special version of Android with less tracking than it is that they'd mandate Google stop snooping on everybody for national security reasons. They take advantage of the data Google collects, the fact that everyone is carrying a mobile wire (mic and camera) filled with radios collecting and broadcasting location info, and that for many people a single device they carry acts as a treasure trove of information on them, who they've been talking to, and what they've been doing.
It’s not so much having a countermeasure but having countermeasures be built in to the system. Similar to a concept called gevulot in the book Quantum Thief.
The only "countermeasures" we can have are "soft" ones - social, political and legal. Convince people to treat privacy as core value, and surveillance as repugnant. Make forms of surveillance illegal. Mandate by law to have surveillance capabilities in devices handicapped by design. But this, at best, only solves the problem for regular people and some of the time, while governments stay stable and sane - the possibility of deeper surveillance is still there, just the choice to perform it seems unattractive at a given moment.