After a few more hours I stumbled upon a solution: Disable Permanent SEO-safe 301 redirect from HTTP to HTTPS in your main domain (the one which happens to be used as my plesk server domain). Once you do that, mailman won't be redirected to HTTPS anymore and the error is fixed.
You can then...
I've got a strange issue with mailman ("Mailing Lists") on the latest Plesk Onyx on Debian 8 with installed Let's Encrypt Plugin.
If I enable "Mailing Lists" on any of my secondary domains and I try to reach http://lists.mydomain.com/cgi-bin/mailman I get redirected to its https counterpart but...