I literally just added the Facebook account 2 days ago to test that integration, and have been having this problem long before that.
Can we focus instead on the Profile About functionality? That, I believe, is the core issue at play here. As I understand it, the Profile About menu type should not trigger a site login, but that is exactly what it's doing for my Registered User profile type. While I'm playing some games with ProfileURL and menu shortcuts to make URLs easy to remember and distribute, I don't believe these are the causes of the problem. What's very curious is that the login prompt is only happening for Registered Users - I have a second profile type for Merchants, which the Profile About functionality works just fine for.
To illustrate this, I created a Profile About menu item for Registered User and the same problem exists. Can you look at
https://sponsorbuy.net/sb/account-menu/christopher? (It's obviously under the account menu). Similarly, I've created a Profile About menu item for a Merchant-type user, which works fine.
https://sponsorbuy.net/sb/account-menu/american-pride. Is there some problem with the way I've defined the Registered User profile type?