BuddyPress.org

Temporary solution how to customize registration form until 1.1 arrives, FYI and my own reference:

Changed this line in function bp_show_register_page() in functions.php in my template:

require ( BP_PLUGIN_DIR . '/bp-core/bp-core-signup.php' );

to

require ( 'custom-signup.php' );

Copied bp-core-signup.php to the template folder, renamed to custom-signup.php.

Go customize!

Unfortunately the custom fields are generated by yet another core function:

do_action( 'signup_extra_fields', $errors );

This action is associated with the function xprofile_add_signup_fields in bp-xprofile/bp-xprofile-signup.php.

Copied the function to bp-custom.php, renamed action and function to custom_signup_extra_fields and custom_xprofile_add_signup_fields.

Used this CSS trick to hide the avatar upload. Will use the same trick to hide the username field.