Hi!
I was surprised to find that I needed to create a separate account here. In many support sites running discourse, the login is actually delegated to another site. For example discourse.ardour.org delegates to ardour.org, running Drupal. Same with forum.fairphone.com, which delegates to whatever fairphone.com is running. 
I am not sure what shop.purism.org is running (Wordpress?), but it would be great to have similar integration.
I’m aware of the possible security issues involved, and I would understand if that was the reason why authentication isn’t shared. But I’m curious to have that be made more clear. Besides, there are ways of doing SSO that do not imply a compromise on site A will compromise site B…
For what it’s worth, there’s a discourse plugin for Wordpress…