Markus Echterhoff

If you have a multisite setup, you normally cannot have the same bbPress forums across all sites of the network. Now you can.
Install this plugin and activate it on the main site and for each subsite that should use the main site’s forums, or network-activate to enable on all sub sites.
If you want both main site and sub site forums displayed on the sub site, set a different root slug and topics slug in the forum settings. After that, both slugs will be known on the sub site and display their respective forums.
BUT! There is a reason why you cannot normally do this and that is because the code base is not really supportive of it. I have monkey patched my way to the goal and I’m doing some evil black magic like hooking ‘query’ and running regular expressions on the query. All of this is only ever done to your forum pages, so be cool, give it a try. If it works for you: great. If it doesn’t: deactivate, relax, look for a different solution (or patch mine).
Profile Note: Profiles are not merged! Favorites, topics started etc show main/sub site only. If you want your users to see all their subscriptions in one place, you’ll have to write some custom code and likely patch my code too.
BuddyPress Note: It does work with network enabled BuddyPress, but they don’t play together nicely because of the BuddyPress/bbPress integration stuff. I have monkey patched this to work. If you do not have BuddyPress installed in /members/ you’ll have to monkey patch my monkey patch, please see the code. And as for the profiles: Same thing as with bbPress profiles.

Multisite bbPress Slave

Make sub sites use the main site's bbPress forums

Robin W

An add-on to the bbPress forum plugin – creates private forum groups
This Plugin creates unlimited private forum groups.
Forums are then allocated to one or more groups, and users allocated to one or more groups.
What this achieves 
unlimited private groups 
Each user is set to a group or groups, and each forum can have any or all the groups associated with it 
Any number of public forums combined with any number of group forums. The group forums can be individually set to public or private. 
Forum title and description (but not topics or replies) can be set to be visible to non-group users, allowing people to see that a forum exists but not access it 
Separate pages can be set to allow redirection of non group users for sign-up or information 
Topic Permissions 
Topic Permissions is designed for sites where users need to have different permissions to different forums. 
For instance the ability for users to contribute to one forum whilst only being able to view another, or only start topics in one forum, or only reply to topics in another.
Example
So if 
User a belongs to group 1 
User b belongs to group 2 
User c belongs to group 3
and 
Forum x is set to allow group 2 
Forum y is set to allow group 2 and group 3 
Forum z is set to allow group 1 and group 3
Then 
User a can access only forum z 
User b can access forum x and forum y 
User c can access forum y and forum z
Restrictions/warnings
The widgets (bbpress) forums list, (bbpress) recent replies, and (bbpress) recent topics SHOULD NOT BE USED, as they will show topics headings and author names for all forums. Replacement widgets called (private groups) forums list, (private groups) recent replies, and (private groups) recent topics are available instead
Works with bbpress 2.5.3 or higher

Private groups

After wasting hours trying to get Skyverge's WooCommerce Memberships to do what I needed (no practical way to protect topics), I tried this and had it doing everything I needed in under 15 minutes.

Setup a group, manually assigned users to that group.
Set the forum to private and assigned that that group to it.
Viola, everything worked exactly as I wanted.

Public doesn't even see the forum exists. Group members can when logged in.  Non-members can't go directly to to topic URL and bypass the protection.

Only suggestions would be:
1. cleanup the settings pages and instructions, they're a bit overly complicated and hard to follow. 
2. some way to trigger group membership programmatically based on a WooCommerce purchase (I know, to specific and I'll probably code it myself for what I need).

Thanks again for an awesome bbp plugin!

Easy setup and protected forums exactly as I needed

For bbPress - Creates private forum groups

Multisite bbPress Slave vs Private groups