Safari prevent all website data storage

How do I prevent any website from storing any of their Website data on my machine?

I have configured Safari as follows:

Website tracking:

Clicked "Prevent cross-site tracking"

Clicked "Ask websites not to track me"

Cookies & Website Data:

Clicked "Block all cookies"

And yet, I still get websites storing their data. See attached screen shots of websites that stored their data on my machine even if I never visited them, after I simply did a search for "weather" on Google and visited only the Accuweather webpage for my results. I do not want any data stored at all on my Safari MBP device.

Frustrated and concerned

Thank you

Message was edited by: psgh