Tong Family

Multisite WordPress is a little strange on registrations of users for commenting. Basically, the default is that you register only at the top level. That is there is a user that works across the entire network. You enable this in the Network Admin/Settings/Network Settings/Registration Settings.

But then you need to add a plugin that let’s you control this at the sub-site level. Once you add the plugin, Network Activate it and then go to the sub-site Users/Registration and you can enable it.

Allow the public to register user accounts on Subsites within a Network (MultiSite) installation.

Source: Network Subsite User Registration – WordPress plugin | WordPress.org