As mentioned above, you can definitely do that with Discourse. In its most basic form you can assign users to groups, and then create categories that only specific groups can access.
Beyond that there are some additional group features that may be useful for your use case:
- Assign group owners (who can invite/remove users from a group without being a site admin)
- Allow @mentions to notify an entire group
- Send PMs to a group
- Automatically assign someone to a group based on email domain
- Add custom flair to specific groups
- Allow incoming email to a group (or category)