It's as mandatory as much as you make it to be.

Unless a legal requirement demanded I provide the information, I do not do it. As a customer of a business I am giving them their money, that's what benefits them most. They don't need to know the information. But if push came to shove, then I would just avoid using whatever requires it unless I have to.

Likewise, I do not have any ID such as a photocard, driver's license or passport. I am not against having these things, but I do not drive (or have the free time to learn) nor travel anywhere so I don't see the necessity in paying for something I wont use. I have had a lot of problems with employers trying to hire me just on that basis. Some residencies wont let me stay without them, yet will give me alternative methods when I ask nice enough.

I usually jump through hoops of using ID verification that immigrants would provide, such as providing a pay check from a former employer containing an ID number, and a proof of residence via a stamped statement over the desk from a bank.

I have an identification number, shouldn't it be enough?