How to change “You must be logged in to post a comment.”

You can try to modify it with the comment_form_defaults filter:

/**
 * Modify the "must_log_in" string of the comment form.
 *
 * @see http://wordpress.stackexchange.com/a/170492/26350
 */
add_filter( 'comment_form_defaults', function( $fields ) {
    $fields['must_log_in'] = sprintf( 
        __( '<p class="must-log-in">
                 You must <a href="https://wordpress.stackexchange.com/questions/170490/%s">Register</a> or 
                 <a href="https://wordpress.stackexchange.com/questions/170490/%s">Login</a> to post a comment.</p>' 
        ),
        wp_registration_url(),
        wp_login_url( apply_filters( 'the_permalink', get_permalink() ) )   
    );
    return $fields;
});

where we use the wp_registration_url() and wp_login_url() core functions.

ps: the info on the comment_form_defaults filter seems to be missing from the Codex.