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.

Perhaps remote neural monitoring is sci-fi thing but I suppose big tech companies use insights and methodologies from neural sciences in their analysis of human behavior based on other types of monitoring.

If the robot takes instructions in human language and emulates somewhat human-like interaction then I think it would not be that hard for any generation to get used to using it. I agree it would take time before it becomes wide spread thing but not because of it being that much alien or new tech with new kind of control but rather because of price. People here compare owning robot to mobile or computer but it would be less affordable, more like car or renting real person for service. (And it would be even more expensive in the beginning) In the same time it may need as much upgrades and replacements as phones and computers... For combination of those factors I think robots ownership would not become that widespread, instead people will rent them.

The robot could actually help your grandma what the the updates...

There are other things that would have problem with people getting used to it. For example Mojo lens, smart contact lenses and other AR stuff. It is totally new user interface. But talking to a robot and telling it what to do seems like no brainer. Tho some pushback could be psychological, the interaction could be uncanny.

Lot of people could not afford to buy even the clean-tron 5000 so instead of buying, they would rent it for monthly fee. When the time for upgrade comes, the 5000 will be replaced with 6000. It is possible to do the same with phones and computers but people don't do this because phones and computers are little more affordable to own. The robot price would not be comparable to computer, it would be comparable to car, personal driver or servant. So imagine company that rents you car for permanent personal use with you permanent personal driver and if you upgrade to super deluxe subscription you can also give tasks to any nearby robots that are not rented for permanent use by someone else kind of like you can use Uber. This model is very likely because robots combine big price with big need for upgrades. Phones and computers are comparably lower price with similar needs for upgrades while cars and renting real person for service is comparably high as price for robot but with smaller need for upgrades and replacement. It is possible that with renaissance of robots, paying real person to do similar work would become cheaper. One would try to outcompete the other.

You could subscribe for personal robot serving you only but you could also subscribe for being able to use any nearby roaming robot of that company. Or you could combine those subscription plans. You could also rent a roaming robot for singular task, kind of like how uber works.

Now there is a question. Would it rather be that some other companies would develop special software for special tasks and provide it to the robot building and renting companies or would it be other way around that certain robot developing and renting companies would rent robots to the companies specializing in providing special services with special software so they would act like middle man between the end customer and the original robot renting company.

Perhaps you would subscribe to renting them and pay monthly. Many people would not have money to buy them, but renting would be possibility. After few years they would just replace your robot with new model. Also if your personal robot is at home doing something and you need some other robot to do something at some other place you are now at, you could do occasional payment and rent roaming robot doing that singular task for you, kind of similar to how Uber works. For sure you could get another subscription plan in which you could use nearby roaming robots any time. You could combine those subscription plans to have few robots rented exclusively for your personal use and yet also be free to use those roaming robots. Also other companies would buy or rent robots from the robot companies.

Also since people are used to rate their experience with online products and well as services like Uber, rating of robots would come probably as well. This could further make way for distopian rating apps like seen in the black mirror episode Nosedive.