Also see https://coveryourtracks.eff.org/
“ Your browser fingerprint appears to be unique among the 311,902 tested in the past 45 days.” yet every cloudflare protected website blocks me, random human checks and also my bank and government is blocked. Mmmmm grain of salt?
those systems probably don't even rely on fingerprinting for those decisions - you just can't deny someone acceess to a service because "they're unique", you're opening a can of worms.
entities that do deny access based on fingerprinting actually do it based on same fingerprints corresponding to a marked visitor (like checking behaviour and marking all subsequent visitors with that fp as bad) - but it's a headache.
what you describe usually has more to do with your IP (range, usage type, country), your useragent or added/modified headers (check any extensions that do this)
i had exactly this happen some years ago when i added a `'` in the UserAgent to test a site for SQL injection and forgot to remove it.