Safari responds with "Safari can't connect to the proxy server" for some websites when I am using the school wifi.

1. Contact your network administrator for help.
2. If you connect to the Internet using a corporate or enterprise network, the network may have a firewall that prevents you from opening the webpage.
3. If your computer or network is protected by a firewall, you may need to specify proxy servers to access some Internet sites. 

If you can’t open a website in Safari on Mac - Apple SupportIf you can’t open a website in Safari on Mac - Apple Support

Try setting up another admin user account to see if the same problem continues. Please post back on whether or not this worked. Also try the Safe Mode. Please post back on whether or not this worked.

Isolating an issue by using another user account 

Safe Mode - About

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor.  Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown. If the log won’t post, try posting it in Pastebin and provide a link in a reply        Pastebin

Etrecheck – System Information

Your Etrecheck report looks okay, but I would uninstall Avast.  It tends to interfere with the computer's operation while providing minimal to no benefit unless you work with Windows files. Most long time posters recommend not using antivirus software or cleaning software such as CleanMyMac. I would also try disabling your Safari extension to see if that makes a difference.

Avast

Avast Un-install

If you make a new admin account and delete it, to include the home folder, that will remove the files from your computer. You might want to leave the account in case you have problems with your account. You can then boot into the new account for troubleshooting.

Does it happen if you are using another WiFi network?

The school WiFi may be set to block certain connections for some reason. Since it works normally other places, I don't think it is s Safari problem.

You are welcome. Thank you for the feedback on what was causing the problem.