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!
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.
You can't vote with just a CPF. The cards aren't issued since 2011, and they didn't have a photo or anything like that. At that time, they were considered tax identifiers only. They moved to printing the CPF number on receipt paper when somebody requested it at the post office when they reached 16-18 years old, usually at the same time when one would request their electoral registration or when requesting an employment booklet. It was a rite of passage to the adult life. More recently all newborns receive a CPF number when they are registered on their birth certificate.
In any case, you have to vote with a photo ID document and you have to scan a fingerprint that was previously enrolled in the electoral justice courts or whenever you renew a driver's license or photo ID. By now 88% of the population have their fingerprints collected for electoral purposes.
In 2023 a law was passed to deprecate state-level ID cards and numbers to use a single federal identifier, and since every economically active person in the country already had a tax ID, the government decided to use the same number.
I do think they cause unnecessary friction for non-residents though, because companies could simply accept passport numbers, as authorized by tax law, but I guess nobody gives this a thought.
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!
Fun fact: CPF was accepted as identification to vote for President!