I understand the concern. I also imagine (I want to be optimistic here, maybe naively so) that most websites wants some form of analytics, probably does not code it themselves and instead of relying on aggregate data like a traffic counter of hits (maybe due to crawlers and other bad agents not respecting robots.txt) then went with somethings fancier. Maybe that fancier tool is trying to mitigate automated traffic with fingerprint detectors.

Well, one can understand and still disagree with it. I suggest contacting the administrator of such website with their concern BUT in the meantime, until they actually do act (which might be never) I suggest to start with self-defense and use dedicated tools e.g. Firefox Enhanced Tracking Protection (you can use a non-Mozilla flavor of Firefox if you prefer) or even more specifically JShelter with its Fingerprint Detector.