Hope this helps someone looking for a solution like I was. This has to do with Safari's long-standing issue with WebGL support. While on latest OSX Safari supports WebGL, if you've been upgrading (like I was) for a while, the setting might still be disabled, hidden in no longer easily accessible preferences...
Verify if WebGL is enabled: https://get.webgl.org
This is how you'll know if Windy.com will work, and how you verify that below steps worked. If it says it WebGL is not enabled, then the following will help you.
Ensure Terminal has Full Disk Access (System Settings > Privacy & Security > Full Disk Access, ensure enabled for Terminal, and restart it Terminal is running)
Run command:
defaults write com.apple.Safari WebKitPreferences.webGLEnabled 1
Verify by running command:
defaults read com.apple.Safari WebKitPreferences.webGLEnabled
It should say 1, not 0.
Restart Safari
Now https://get.webgl.org should show it's working, and Windy.com should work as well.