Why don't WPMU Membership and Headway Community Builder block get along?

When I activate Headway Community Builder (http://headwaythemes.com/extend/addon/community-builder/) and WPMU's Membership plugin at the same time it causes BuddyPress activity updates to double-post. When either one is active with the other inactive activity updates work just fine.

I really want to use both of them in tandem. Any ideas what could fix this?

I've also posted this situation on the Headway forums.