Activity Tab - Connections

Can you only view the Activity Tab of  members you are connected too?
Is there an option for this?
Or is this intentional?

It's not limited to connections. Can you be more specific about what your issue is?

I can only view the Activity Tab of members I am Connected to.
If I visit a Profile of a Member I am NOT connected to, their Activity Tab is not displayed. 
And yes, these members do have Activity in their profile.

There's no access permissions for that in CB Activity. The connection checks that do exist are for commenting on or liking content. My best guess is you've privacy controls enabled for the Activity tab in CB > Tab Management and the activity tabs privacy is set to Connections. Did you install CB Quickstart? If so then those privacy controls do exist and do default to connections. You can adjust the defaults or turn off privacy controls in CB > Tab Management > Activity > Integrations > CB Privacy.

Display is set to Default>Same as Global
CB > Tab Management > Activity > Integrations > CB Privacy>Display> Default>Same as Global

Does the Activity Plugin have anything to do with this?

I believe you still have my login info.

The hosting service loaded CB for me so I presume they used Quick Start

If default is "Same as Global" then it'll use the default from CB Privacy > Parameters > Privacy > Display.

This all assumes the profile didn't save a privacy rule yet. Edit the profile and check the privacy of the Activity tab. It will probably be under a centralized Privacy tab since you've CB Quickstart applied so all privacy controls are configured there. The privacy for the Activity tab is likely set to Connections. If this is a live site then that's what the user decided they wanted their activity privacy to be though.

If you don't want privacy rules at all for the activity tab then you can disable privacy controls by editing the Activity tab in CB > Tab Management then under Integrations > CB Privacy turn off privacy controls.

I believe you still have my login info.

We do not do install reviews every time you have an issue unless we suspect a bug that we need to investigate. Please keep in mind we're not a contracted personal web developer, which would cost considerably more, so we're limited to what we can assist you with.