How can I show custom fields in the loop only to specific user roles?

Question

You can use current_user_can() and is_user_logged_in() to validate current user:

<?php if ( is_user_logged_in() && current_user_can('role') ) : ?>
    <span style="font-size:16px">
    <strong>Currently reading:</strong> <?php the_field('book_name'); ?> (<?php the_field('book_year'); ?>)<br/>
    <strong>Currently seeing:</strong> <?php the_field('movie_name'); ?>"><br/>
    </span>
<?php endif; ?>

Make sure to change role to your preference and take a look at Codex for more info.