@vabvarun – Thanks for your suggestion, but I need that option because only logged-in users has access to the website.
However, you gave me an idea :-)….I solved the issue using 2 lightweight plugins: WPS Hide Login to choose my own login-url (which is better) and Restricted Site Access to replace the BuddyPress funtion and choose a custom redirect login-url. Also, the login-page is loading a little faster with these plugins.
Problem solved. But it would be great when BuddyPress would offer those small features as well.