Display page only if user registered before a specific date

This is a basic function to get the current user and compare it with a custom DateTime to see if the user registered earlier or later:

function wpse_219284_registered_before( $date_time ) {

    $user = wp_get_current_user();

    $registered_before = false;

    if ( $user instanceof WP_User ) {
        $registered = new DateTime( $user->data->user_registered );
        $limit = new DateTime( $date_time );
        return $registered < $limit;
    }

    return $registered_before;
}

Be aware that this defaults to false for e.g. unregistered users.

You can e.g. use it in your templates like this:

if ( wpse_219284_registeredBefore( '2015-06-25' ) ) {
    the_content();
} else {
    echo "Registered too late to read this. The early bird catches the worm.";
}