Still having problems.
1. Login as customer, go to /ProfileView.aspx of customer - ok, go to /ProfileView.aspx of manager - no properties are displayed.
2. Login as manager, go to /ProfileView.aspx of manager - ok, go to /ProfileView.aspx of customer - no properties are displayed.
3. Logout, set AllowAnonymousUsersToViewMemberList option in web.config to "true", go to /ProfileView.aspx - see WebSiteUrl property for all users and nothing more (except a message that some properties were hidden as I am not logged in).
P.S. UserProfile page works properly now.