Whatever you do there will always be uniquely identifiable information (if not an id, a fingerprint) on your machine.
If you want to escape that, you have to use dedicated privacy-enhancing tools / browsers, but even then, it's very likely that you can still be identified by motivated adversaries.
It doesn't mean you have to give up, but, if such id is necessary for technical reasons in systemd (I guess it is), I wouldn't worry too much.
When you go really hard with the privacy-enhancing tools, you can potentially just make yourself even more visible. When you're so far outside the normal way a user looks you're making yourself even more unique than if you had normal-ish looking identifiers.
It can take a lot of effort to make yourself truly just blend in and disappear.
No security is perfect; there is always a way to bypass it. But security can be highly valuable.
> motivated adversaries.
This sounds like you're referring to state actors and intelligence agencies, but really this applies to the entire advertising/surveillance industry of people trying to sell you a new flavor of soda.