BuddyPress.org

@airrykah deactivate BuddyPress. It depends on your WordPress installation. Check if your install is sending out activation emails to those registering. Find resolution for your email problem at WordPress.org forums before activating BuddyPress.

If your WP activation email is working, deactivate any BP registration plugins and see if regular registration works.

Edit – there’s also a workaround, see if this works for you – https://codex.buddypress.org/getting-started/faqs/specific-faqs/#register