Hi Ross,
It’s not, unfortunately. Here is my search.php page below. My search form is the <?php get_sidebar('filter'); ?> widget.

<?php
/**
 * The template for displaying search results pages.
 *
 * @package _s
 */

get_header(); ?>

	<section id="primary" class="content-area">
		<main id="main" class="site-main media" role="main">

		<?php get_sidebar('filter'); ?>
		
			<?php if ( have_posts() ) : ?>
			
			<div class="entry-content">
				<?php /* Start the Loop */ ?>
				<?php while ( have_posts() ) : the_post(); ?>
						<?php
						/**
						 * Run the loop for the search to output the results.
						 * If you want to overload this in a child theme then include a file
						 * called content-search.php and that will be used instead.
						 */
						get_template_part( 'content', 'search' );
						?>
				<?php endwhile; ?>
			</div>
				
			<?php else : ?>
				<div class="entry-content">
					<p class="no-results"><?php _e( 'It seems we can&rsquo;t find what you&rsquo;re looking for. Broaden your search by eliminating a selection or try a general search.', '_s' ); ?></p>
					<?php get_search_form(); ?>
				</div>
				
			<?php endif; ?>
			
		</main><!-- #main -->
	</section><!-- #primary -->
	<div id="pagination-holder">
		<?php paginate(); ?>
	</div>
<?php get_footer(); ?>

Alright, so last update… good news! Please excuse my explanation if it’s unclear at all, I’m a bit of a n00bie dev.

The issue was occurring on a callback. The popstate was being called on Safari upon page reload, but not in Firefox or any other browser (surprisingly, Chrome wasn’t having an issue). By commenting out var $data_obj_get = $(data);, I stopped the code from re-adding the html (below)

var $ajaxed_search_form_get = $data_obj_get.find('*[data-sf-form-id='+form_id+']');
$thisform.html($ajaxed_search_form_get.html());

and as a result, initSearchForms(); was not being overridden by this bit of code. By calling initSearchForms(); again after the two lines of code above, and uncommenting var $data_obj_get = $(data);, the comboboxes were being created after the html purge and re-write.

So all is well! Thanks!