Many payment providers would want websites to implement CAPTCHA for blocking spam and fraud attempts.
I’m sorry, but you’re just going to have to walk to a store and pay in cash if you don’t want to have any data tracking done at all. Online you’ll often have to pick one or the other: data tracking, or flimsy security/data protection. The phone solution is appropriate in my humble opinion, but you’re welcome to hold your own views on your principles. If you’re hard set against a company tracking ANYBODY via 3rd parties to that level, then I bet you will be very hard-pressed to ever find a computer through an online marketplace from ANY company that will fit that bill perfectly and suits your other needs.
Whew! All clear, it’s a meme. Pack it up, people.👮♂️👮♀️