This may actually close the class divide a little.
The thing with privacy is the more wealthy you are, the more valuable it is. For example, if I want to sell something, I will want to target the wealthiest first. Same thing for scammers, and newspapers will follow celebrities. Who care about the poor, there is no money to extract from them.
So let's get back to the private shopper. A rich and famous man will want to hire a private shopper, because he knows that if he is found in a shop, he will be bothered by people who are after his money and fame. His privacy is worth a lot, to him and to others.
The private shopper is likely to be of a more modest status, he can go shopping without being bothered, he may be tracked by robots and end up with personalized ads, be part of some statistics, whatever, but no one will stop him for an autograph or some special favor.
So when the rich man pays the private shopper, with a little extra for his discretion, that's resources that go from the wealthy to the "rest of us".
The same can be said for loyalty cards. The one who can afford not to use loyalty card will earn the shop more profit (because no discount), meaning that it can offer bigger discounts to others.
It is as if a unit of privacy is proportional to your wealth. The amount of privacy a rich man will get by paying $1000, a poor man can get it for $1. In the same way that it is much cheaper to secure a penny than a gold bar, because no one will want to steal your penny.