May i know did you try temporary turn off your membership system on your site and see whether system can able to assign the newbie badge to the new user?

If can, mean something is not right from this membership system.

By the way, can I know when the user subscribe one of your site existing plan, did it automatically activate their account after they pay?

Yes the badge works fine when using ES for registration.

And yes, users are automatically logged in when they complete their registration.

Hey Peter,

I think you have to consult with this membership Pro developer regarding this and see how they activate this user account once system detected this user already done the payment.

By right, Easysocial original registration without membership system, it will go through this saveStep method under this file
JoomlaFolder/components/com_easysocial/controllers/registration.php , then log this newbie badge for this new user.

By the way, this is the following code how Easyblog log the badge for the user.
[gist type="php"]
$badge = ES::badges();
$badge->log('com_easysocial', 'registration.create', $my->id, JText::_( 'COM_EASYSOCIAL_REGISTRATION_BADGE_REGISTERED'));
[/gist]

Currently i have no ideas why it doesn't work after integration with this membership Pro extension, since this membership Pro is not developed by us, perhaps you can keep in touch with them again and see how it goes.