You are crazy.
Back in the good old pre-Internet commerce days, when you'd go in person to a store, you did not have a reasonable expectation that the owners/employees will forget you once you're gone. If you didn't want the owner/employees to know, you'd get someone else to go in on your behalf.
If you don't want McDonald's to know, get someone else to buy for you.
No one is making you install that app.
Long before smartphones were a thing, I refused to join any "loyalty program", for reasons similar to the ones you're voicing.
I went through multiple periods where I paid only cash, reserving CC's only for online purchases. I even paid most of my utility bills in cash (showing up in person at the office). For something as unimportant as fast food, it is totally doable.
If you want convenience (CCs) or benefits (loyalty programs), don't expect to have your cake and eat it.
Not if they don't like you.