If you don't put the information out there, then they won't have it. It's a simple cause and effect relationship. Not giving up this information will likely cause you to not be able to use some services, however you have no inherent right to access services run by private parties. They are offered to you under certain conditions, and if you choose not to comply with those conditions, you are free to not use the service. With regard to "shadow profiles," simply use incognito mode if you are this worried about it.

Let's be clear that this law won't pass, certainly not as it is written. In the US, it's perfectly legal for websites to track your behavior. Should you object to this, you have a simple remedy: use incognito mode.