Do you refuse to watch age-restricted films in the cinema because the owner of the cinema might have a record of what you've watched? Age-restricted websites are no different. You can comply with the access requirement, or refrain from using the service. It's your freedom of choice.
No-one is forcing you to watch 18-rated films at the cinema, or purchase alcohol or drugs, or view pornographic material online. If you don't like the requirement to prove your age by presenting some form of ID, then all you need to do is voluntarily refrain from these and any other age-restricted activities.