BuddyPress.org

Seems like this should work:
-Create a Child Theme: https://codex.buddypress.org/how-to-guides/building-a-buddypress-child-theme/
-Copy the file in the default BP theme folder/registration/register.php and save it in your new child theme folder as a page template (or you could just overwrite the index.php)
-Create a New Page that uses that page template
-Go to Settings–>Reading and set the new page you created as a “Static Page”

I saw a plugin to do a sidebar registration for WordPress a while back, but I’m not sure if it works for BP or not.