"Editors in good standing whose editing is disrupted by unrelated blocks or firewalls may request IP address block exemption, which allows editing on an otherwise-blocked IP address... If you will be editing using an anonymous proxy, including a VPN service, you must send your request to..."
See https://news.ycombinator.com/reply?id=21700802 and https://en.wikipedia.org/wiki/User:Guy_Macon/Wikipedia_has_C...
Re: "I habitually use a VPN, and Wikipedia does not let me contribute (specifically, edit pages), even if I am logged in."
You can request permission to edit Wikipedia through a VPN.
See https://en.wikipedia.org/wiki/Wikipedia:IP_block_exemption
"Editors in good standing whose editing is disrupted by unrelated blocks or firewalls may request IP address block exemption, which allows editing on an otherwise-blocked IP address... If you will be editing using an anonymous proxy, including a VPN service, you must send your request to..."