ISSUE SUMMARY:
This is similar to another issue I experienced recently with emails not going to some users when sending a private message. I requested to be friends with materry and he did not receive the request. Most of my users were imported from another system so they did not have params set in the community_users table. I have now updated the records to have settings. I am not sure if this is related but the params should be good now.

STEPS TO REPLICATE:
1 Request materry to be friend
2 Check Monitor Mail queue
3
4
5
RESULT
No email in queue.

EXPECTED RESULT
Email sent to materry to be friend.
BROWSER

Hi, John.

I followed your replication steps. Result: i.imgur.com/QvCp2T9.png
And email appear on the queue.
It also appeared (without any issue) when I sent friend request to my user (I crated).
i.imgur.com/Ur6m8mt.png

Conclusion is that this feature seems to work fine... but you may have mess in database...
Moving database from one to another is always risky... and rather not recommended.