Public Open Membership, Join behind the scene?

You have two issues to work through.

1.  A user who is not a member won't have permissions to perform certain actions, so they won't see those options to even interact.  You can overcome that by giving some or all of the same permissions that the Public Open member role has to the Registered User role in that group.

2.  You will now need an automation that runs for each of those actions (i.e. ForumThread-BeforeCreate, ForumReply-BeforeCreate, etc.).  That automation would check if the author is a member of the group, if not add their group membership.

This is great, yeah our issue is that we current have Registered Users in Public Open, so when a user views their groups, it all our groups. 

This is great, yeah our issue is that we current have Registered Users in Public Open, so when a user views their groups, it all our groups.