Is it possible to make one of two custom fields in Custom Post Type UI Required but not the other?

You should use Advanced Custom Fields. If I understand what you want to do correctly, you can add a Select Field with Radio Buttons, and then build conditional Page Link and Text (for the URL) Fields that appear based on the Select Field button.

You would then build an if/else statement in the code:

<?php if(get_field('page_link') == "internal"): ?>
  <a href="https://wordpress.stackexchange.com/questions/147695/<?php the_field("internal_page_link'); ?>">Page Link</a>
<?php else: ?>
  <a href="<?php get_field('external_page_link'); ?>">Page Link</a>  
<?php endif; ?>

You can set the two options up to be conditional based on the selected button from select field.

Also note in this example, you should use get_field for the Text field. This will return it as a string and not output text to html.