[peterspliid]

I had the same issue, and since I couldn’t find a solution, I had to make one myself. I thought I’d share.

Add the following to your functions file

function fix_private_message_login() {
    Global $bp;
    if (isset($bp->canonical_stack['component']) && $bp->canonical_stack['component'] == 'messages' && !is_user_logged_in()) {
        header('Location: ' . get_site_url() . '/wp-login.php?redirect_to=' . $_SERVER['REQUEST_URI']);
        die();
    }
}
add_action('bp_do_404', 'fix_private_message_login');

If you’re admin, you will most likely be redirected to the admin panel after login (instead of the message), however for all other users, it will redirect you to the message.