Like pre-paid cards. Or those banks that generate new card numbers for every transaction. Or having the cards be owned by some sort of company instead of an individual person?
Phones would be the same thing: you get temporary numbers that redirect you do the real one. I have no idea how feasible this would be, but I bet some similar service exists for businesses.
Why yes you can, and you get proxy privacy as a result.
The problem is that this information is valuable to the bank and the state, and the only way to keep their nasty little noses out of that trough is not to generate that information, and that means no phone, cash payments. The various technical solutions mentioned in this thread miss the point that the problem itself is not technical, it is sociological and political.
Almost everyone will eventually decide that their privacy is not worth the cost of the loss of their phone. That's their choice, but one should at least recognise that that choice has been made.
I don't agree that it's all just about "using phone and credit card". You can always just use dumb phone (or no phone) and fiat money.
My question is more about removing what's already there (Google, Facebook and other services).
Let's say the data you already generated stays there.
What can I do from now on to not generate more?
AFAIK many online shops also upload their customer information to Facebook, I use the same email for FB and online shops, so there's Zuck making money off that data of mine. But even without using the same email, if many shops have your name/shipping address and they all upload it to FB, FB has a profile of your real name and address [do the shops upload these?] and your online shopping preferences.
In my mind, if I worked for FB, it would be easy to build a shadow profile. Your friends use WhatsApp/FB Messenger on their phones? And they uploaded their address books? Well, Zuck can see there's a friend network with FB/WA accounts who have each others' numbers, and Zuck can see they all have this same phone number for their "not-in-Zuck's-network" friend Eslus (again, if your friends stored your real name in their address book, Zuck also has this information). If there are 4 people known to Zuck, and one of them uploads pics where there's 5 of you, through deduction Zuck's algorithms can see "Ah, the 5th person must be Elsus, according to this time and geo-tag, all 5 were at a Lady Gaga (or whoever) concert, so that means Elsus must also like Lady Gaga's music.".
I knew the way things are interconnected nowadays is unprecedented in history. This insight brings me back to one of my ideas I had few weeks ago. Hold on with me since my technological background is certainly lower in several magnitudes than yours.
Given that Facebook just won't delete anything it has stored about you I tried to think about other ways to decieve it. It might be impossible but what about generating alternative accounts with slightly different information. Eg. creating several (hundred?) profiles that are basically decoys, pumping "input noise" to the system eventually confusing the algorithms.