I think Conditional Menus would need tweaking to understand that the BP pseudo pages where the menu needs to display: Ask the developer.
Update: Found out that the reason is BuddyPress supporting Primary Nav menu only.
Is there a way to add support for different menus as well? Thanks.
Have you looked at https://wordpress.org/plugins/nav-menu-roles/ that’s what I use to only display some menus to logged in members
Yes, I’m using this plugin as well and it’s great. The issue, however, is that I’m looking for a way to display a specific menu to the community (BuddyPress) members. One that’s different to the primary website menu.
All I can suggest is that you raise a new feature request on https://buddypress.trac.wordpress.org/
If anyone is looking for a solution – sorted this out creating a custom header with the nav menu I want.