If you install BuddyPress on the main domain you can use the Display Widgets SEO Plus Plugin https://wordpress.org/plugins/display-widgets-seo-plus/ (I’m the developer) to show/hide widgets on specific sections of a site.
Just released version 1.1.0 which includes specific widget logic support for BuddyPress/bbPress, could set the widgets for the BuddyPress parts of the site to NOT load on non-BuddyPress sections, this would stop some ‘bleed through’ of content from BuddyPress to the rest of the site.
That being said, from an SEO perspective (my background is SEO) there are other issues that could leak out to potential Google visitors.
The 6 links for the WordPress Plugin Repository listing are benign, but if there was an adult section of WordPress it could be listed as a sitelink.
From a WordPress perspective there’s also the core WordPress Search functions. The Static Pages that BuddyPress uses for ‘holding’ the BuddyPress specific output can be found via a search. If you have the default BuddyPress setup try using the WordPress Search Form to search for the word “Members”.
This will find your BuddyPress Members Directory Holding Page.
Same result with “Registration”, “Activate” and “Activity”.
It’s difficult to prevent bleed through of different types of WordPress content, so if your client is conservative I’d suggest a sub-domain/other domain to play it safe and manually add interlinking via Text Widgets and Nav Menu Links.
