No problem. Instead of

$to = $_POST['register_email'];

Please try

$to = '[email protected]';//

Use a valid email there and test if it work or not?

Thank you.
I see that you have spaces allowed in username. It may be one of the reasons.

Can you please disable Message Privacy and post here. We haven’t tested message privacy with username compatibility, so need to know that.

Thank you
Brajesh

Hi Graham,
It’s dood to know that. All the best with your community building 🙂

Hi Dandy,
Please upgrade to 1.0.8(It was updated a few months ago) and then let me know if it causing any issue. I tested with BuddyPress 2.7.2, BuddyPress Message Privacy 1.0.8 and WP 4.6.1 and with the above code in my bp-custom.php, It is working as expected.

Regards
Brajesh

Hi Julien,
I have cleaned your code a little bit.
Can you please try this?
http://pastebin.com/nzNL7zDY

Is your sites normal email working?

Thank you
Brajesh