I reorganized your code a bit so that I could better see what was going on, for me it makes it a little clearer. This is what I came up with. Hopefully you can see the changes I made to the logic.
<div>
<!-- Check for parent repeater row -->
<?php
if (have_rows('menu_sections')) {
?>
<ul class="nav nav-tabs" role="tablist">
<?php
$row = 1; // number rows
// Step 1: Loop through rows, first displaying tab titles
while( have_rows('menu_sections') ) {
the_row();
?>
<li role="presentation" class="list-unstyled<?php
if($row == 1) {echo 'active';}?>">
<a href="#<?php
echo $row; ?>" role="tab" data-toggle="tab"><?php
the_sub_field('section_title'); ?></a>
</li>
<?php
$row++;
} // end while have rows
?>
</ul>
<?php
reset_rows();
?>
<div class="tab-content">
<?php
$row = 1; // number rows
// Step 2: Loop through rows, now displaying tab contents
while (have_rows('menu_sections')) {
the_row();
?>
<div class="tab-pane <?php
if($row == 1) {echo 'active';}?>" id="<?php echo $row; ?>">
<?php
while (have_rows('section_items')) {
the_row();
// Display each item as a list
?>
<ul>
<li class="list-unstyled"><?php the_sub_field('dish_name'); ?></li>
<li class="list-unstyled"><?php the_sub_field('dish_description'); ?></li>
<li class="list-unstyled"><?php the_sub_field('dish_price'); ?></li>
</ul>
<?php
$row++;
} // end while have rows section_items
?>
</div>
<?php
} // end wile have rows menu_sections
?>
</div>
<?php
} // end if have rows
?>
</div>
