Earlier quoted context omitted.
Just a note 301s are super sticky and browsers cache them even across incognito modes. Your best bet is to use a new browser after reconnecting to avoid false results.
Really? That seems like a fantastic way to fingerprint people. I would be a bit surprised if that was the case... (Fingerprint usage: have https://myfingerprint.example.com 301 to https://myfingerprint.example.com/unique_id_3b136c1cb , then embed https://myfingerprint.example.com in an iframe and see which request is made.)
I still never use 301s for that reason. Things may have changed, but I dare not try!