They have quite a privacy policy: https://www.apple.com/legal/privacy/en-ww/
Which makes me think of Paul Graham's essay when he says "Lucy, you've got a lot explaining to do!" http://www.paulgraham.com/hp.html .
I don't think you can pay on the App store without a credit card. Most top tier Mac developers have their software available for purchase outside of the app store, but it'll certainly get tied to your hardware IDs. Providing false information probably technically violates the terms of service, but I haven't checked. You can probably use gift cards and fake information.
I'd say maybe possible, depending on how you construe the problem.
It beats Windows, but if you care that much about privacy, you'd have to use an ethics (freedom) motivated OS. Microsoft certainly wants you to create an account to install Windows and seems pretty motivated to get something going with tracking you. I've started considering running Linux on M1. I don't think you have to compromise your privacy more than anywhere else to buy Mac hardware, per se.
I think you have to separate the hardware issue from the software issue, although the Mac platform seems a bit less compelling if you just want to install Linux/FreeBSD/whatever.