Catalina: HTTP downloads in Terminal stall without sudo
After some more digging (using lsof), I found the culprit to be Sophos AntiVirus.

If you run into a similar issue, open Sophos preferences, disable Live Protection and anything enabled in Web Protection.

Then try running wget (or whatever was blocked) again.

Once that works, you can reset Sophos preferences to their defaults again and check if everything still works.

Looks like a bug in Sophos AntiVirus to me.