The sledgehammer way would be to simply remove_action this callback: https://github.com/WebDevStudios/BuddyPress-Registration-Options/blob/master/includes/core.php#L779-L813
Looks like I didn’t include the “Pending Membership” text as part of the filters that I do provide, like I probably should have. Will make note of that detail.
I know the wp_mail() function has a filter right at the top that you could intercept it at, if you wanted to.
Cool – thats great, removed the action in functions.php
// Remove pending email alert
remove_action( 'bp_core_activated_user', 'bp_registration_options_notify_pending_user', 10, 3 );