The CNIL's page says that standard contracts do not offer adequate protections and as such are insufficient.

No such thing. You can't sign away your rights. The end.

If you're in the EU you don't have the right to give your IP address to a US company?

Your own IP address?

What's the point of having personal data if you aren't allowed to make decisions about it

You can absolutely choose to share your data with an US company, but you can also withdraw consent five seconds later, making it illegal for them to further process the data. The point is, that it is your personal data, and only you get to say what can and can't be done with it. That right can't be signed away.

European laws have a different approach regarding most individual rights. They are socially defined and distinguished from ownership.

Your body for instance is probably better protected in terms of chemical additives, healthcare and now pregnancy choices, but you can't easily sell body parts or be a surrogate.

You do but you can't be forced to agree, including by not being able to use the service if you decline.

I'm not sure about that second part.

If a service operator decides they don't want you using their service, they don't have to let you use it. That only gets murky around protected characteristics (race, sex, gender, orientation, etc) which "privacy" is not.

They could make access contingent on being allowed to process your data.