Before those robots come there would be AR smart contact lenses and other wereable accessories, that would replace phones and would infiltrate into our privacy way more then phones ever did monitoring your activities and surroundings through wereable cameras, microphones and other sensors. (Google mojo lens) Also smart home devices would become more widespread and integrated thing before those robots come. Both of those technologies are less difficult and would be more affordable then robots so robots would come later. Concerning privacy the former technologies would already invade to it strongly. Humanoid robots would not add much at that point.

Next big thing after that causing danger to privacy in new level would be nanobots. This is very sci-fi now but there exists theoretical concepts like smartdust, neural dust, claytronics and utility fog and some companies try to work on some very early things. Basically imagine everpresent colony of nanobots penetrating every corner of world and especially biosphere and technology, they could manipulate other matter on molecular level or form new solid structures out of themself as if suddenly the air around you (full of nanobot dust) solidify to something. They could also move things around. Most importantly those nanobots would live inside living organisms. Medical nanobots would help with monitoring health as well as with healing and treatment. Some nanobots would be meant to help with neural medical conditions. Theoretically nanobots would be able to communicate directly with brain, with one another as well as with other electronical devices or nanobots in brains of other people. This means you could control electronical devices by thoughts, use nanobots abilities by thought and recieve information directly as stimulus to your neurons. Now how this is concern for privacy is clear. Also hacking some nanobots or some nanobots getting bug could get really messy for organism.