Damian

Based on crashutah, apeatling https://wordpress.org/plugins/bp-disable-activation/ Disables the activation email and automatically activates new users in BuddyPress under a standard WP install and WPMU (multisite). Also, automatically logs in the new user since the account is already active.
Basically i updated the plugin and added some features like:
-Option to turn off automatic login 
-Redirect options after account creation
Known Bugs: 
-Doesn’t do the automatic login if you allow blog creation during the user creation in WPMU (multisite)
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Bulk plugin installation tool, import WP favorites and create your own lists (<a href="https://wordpress.org/extend/plugins/wpfavs/" rel="ugc">https://wordpress.org/extend/plugins/wpfavs/</a>)
<h4>Increase your twitter followers</h4>
Increase your Twitter followers with Twitter likebox Plugin (<a href="https://wordpress.org/extend/plugins/twitter-like-box-reloaded/" rel="ugc">https://wordpress.org/extend/plugins/twitter-like-box-reloaded/</a>)
<h4>WordPress Social Invitations</h4>
Enhance your site by letting your users send Social Invitations (<a href="http://wp.timersys.com/wordpress-social-invitations/?utm_source=social-popup&utm_medium=readme" rel="nofollow ugc">http://wp.timersys.com/wordpress-social-invitations/</a>)

BP Disable Activation Reloaded

The plugin is still working. It would better if you work on autologin after register

Still Working

Based on crashutah, apeatling plugin Disables the activation email and automatically activates new users in BuddyPress under a standard WP install and …

shawfactor

All this plugin does is is change the buddypress signup activation process such that:
When signed up user activates their account, it makes them logged in
Once that user is logged in, they are redirected to their profile
Like this plugin? Please consider <a href="https://wordpress.org/support/view/plugin-reviews/lh-buddypress-login-on-activation/" rel="ugc">leaving a 5-star review</a>.
Love this plugin or want to help the LocalHero Project? Please consider <a href="https://lhero.org/portfolio/lh-buddypress-login-on-activation/" rel="nofollow ugc">making a donation</a>.

LH Buddypress login on activation

Makes your buddypress signup process seamless by automatically logging on users who activate their account.

BP Disable Activation Reloaded vs LH Buddypress login on activation