Counting unique web site visitors without using cookies, UIDs, or fingerprinting

Just create a uuid and store it in a cookie or local storage. You're fine, you're allowed to do this. As long as you don't relate it anywhere to some other information and treat it as "some user" you're on the safe side.

It's only ever an issue when you generate the uuid based on device parameters or use the same uuid across multiple sites (that don't belong to the same entity).

The demo works in chrome, but not in safari. After 3rd reload, it goes back to 1, instead of 3.