You are never forced to provide your CPF for trivial things, it's completely optional and it's usually used for convenience (easier to get a refund later, for example) and even for people to get some tax discounts in some States. I've never seen anyone showing a passport in Brazil. Though I'm Brazilian, my CPF had been cancelled after more than 10 years I didn't use it (since I haven't lived there in more than 20 years) but that never caused me any inconvenience.
Fun fact: CPF was accepted as identification to vote for President!
As a tourist a few years ago I needed to provide a CPF to buy soccer tickets online in Sao Paulo. Intercity busses also required one to book online. Neither accepted anything else like a passport. It was... inconvenient and not optional for those things!
> never forced to provide your CPF for trivial things
I had to provide my CPF to sign up to a gym.
Signing up for most things requires a CPF, some offer a passport option but a lot don't. Trying to make a payment online is also sometimes blocked by requiring a CPF. The fact that you can vote with it is just another point for why it shouldn't be treated like an email, those cards look incredibly easy to fake.