when you edit a Customer Community config and click the Email tab, you get the following setting:
However, I've found that when I uncheck this checkbox, that same email template is still sent to new members (at least when they are created via the "Enable Customer User" button on the Contact page).
The org I'm seeing this in only has one single Community, and the "New Member Welcome Email" template referenced above is not referred to anywhere else that I can see.
Is this a bug in Communities, or does unchecking this email have some different/subtle effect that I'm not aware of? (Like for instance perhaps it only affects self-registered users, which are not available in the Community I'm using?)