So in terms of our plugin here, we only send an email in the following conditions:
To the users themselves:
Message saying they’ve been approved or denied based on moderation action by moderator. Subject line will be either “Membership Approved” or “Membership Denied”.
Message saying their account is pending moderation. Subject line will be “Pending Membership”.
To the administrators:
Message saying there’s a new member to moderate. This one is sent upon user registration, but not user activation. Subject line will be “New Member Request”.
Any emails that you’re trying to control are going to be from BuddyPress core or potentially other plugins involved in your site. You can definitely make use of our functions to control those, but you’ll need to find ways to hook into that process.
If you can confirm any of those subject lines match the ones you’re testing out and want to remove, let me know which and I’ll double check our code for you.