Hi Frank,
Thank you for posting here.

There is a bug in BP Nouveau template that cases it.

I have updated the code with the fix. Please use the following code

function buddydev_filter_private_message_button_args( $args ) {

	//if the user is logged in, we don't need to do anything
	//Also, I am only handling it for profile buttons here
	if ( is_user_logged_in() || ! bp_is_user() ) {
		return $args;
	}

	$user_id = bp_displayed_user_id();

	$args['must_be_logged_in'] = false; //show for non logged in too
	//and redirect to our custom url containing the user id
	$args['link_href'] = wp_login_url( site_url( '?message-redirect=' . $user_id ) );

	return $args;
}

add_filter( 'bp_get_send_message_button_args', 'buddydev_filter_private_message_button_args' );

/**
 * Fix for nouveau.
 */
add_filter( 'bp_nouveau_get_members_buttons', function ( $buttons ) {
	if ( ! isset( $buttons['private_message'] ) ) {
		return $buttons;
	}

	$buttons['private_message']['button_attr']['href'] = wp_login_url( site_url( '?message-redirect=' . bp_displayed_user_id() ) );

	return $buttons;
} );

/**
 * Redirect to the send message when the user logs in
 **/
function buddydev_redirect_to_send_message_on_login() {

//make sure it is our url set in previous step
	if ( ! is_user_logged_in() || empty( $_GET['message-redirect'] ) ) {
		return;
	}

//redirect to PM
	$user_id = absint( $_GET['message-redirect'] );
//let us make sure that user exists
	$user = get_user_by( 'id', $user_id );
//can not PM to invalid user
//also you should not send message to yourself
	if ( ! $user || $user->ID == bp_loggedin_user_id() ) {
		return;
	}

	$url = bp_loggedin_user_domain() . bp_get_messages_slug() . '/compose/?r=' . $user->user_login;

	bp_core_redirect( $url );
}

add_action( 'bp_template_redirect', 'buddydev_redirect_to_send_message_on_login' );

Regards
Brajesh