NipponMonkey

This plugin makes your BuddyPress community private. You can control which areas of your site are accessible to logged out users in two ways, “restrict site access, but allow some public pages” or “allow site access, but restrict some private pages”. This plugin also can block widgets from logged out users and block all RSS feeds.
In the default mode (restrict access, but allow some public pages), logged out users only have access to your homepage, or access to a list of pages/areas that you’d like to make public. Logged in members have full site access.
If you visit the community when you’re logged out and you’re visiting a private page, then you’re redirected to a landing page of your choice (defaults to the homepage).
You can set uris that are accessibly to non-logged in users using a special config php file – no database calls are needed.
In the alternative mode (allow site access, but restrict some private pages), logged out members have full site access, but you are able to make some pages/areas of your site private – so only logged in members are able to view them. This is the opposite to the default mode.
In the default mode, the plugin blocks all of your widgets from being visible to logged out users. This stops possible private information from being seen when non-logged in users visit your site. 
You can change the config file so that some of your widgets are still displayed. In the alternative mode, all widgets are shown but you’re able to block widgets that should only be displayed to members.
Also, all RSS feeds are blocked by default too.
You might also like to change these setting in your WordPress and BuddyPress settings.
<ul>
<li>BP Setting: Hide admin bar for logged out users? = YES</li>
<li>WP Setting: Membership – Anyone can register? = NO</li>
<li>WP Privacy Settings: Site Visibility = I would like to block search engines, but allow normal visitors</li>
</ul>
See the FAQs or the example config file in the download for more information on configuring this plugin.
You can see an example of this plugin working in the default mode here: http://www.englishpubpool.co.uk/bppc_test/about/
<ul>
<li>Please note, this plugin requires PHP 5.</li>
</ul>
If you’d like to ensure that users don’t stay logged into your site after a set period of inactivity (for security reasons), then you could use this plugin:
<ul>
<li>Inactivity Auto Sign Out plugin: https://wordpress.org/extend/plugins/inactivity-auto-sign-out-plugin/</li>
</ul>

BuddyPress Private Community

This plugin makes your BuddyPress community private. Only logged in members can view the social areas in full. You can configure the default settings.

chiilog (Chiaki Okamoto)

If you view a website without log in, WordPress redirect to the login page

WP view login only

If you view a website without log in, WordPress redirect to the login page

BuddyPress Private Community vs WP view login only