Looks like I found a solution for anyone who wants to have JUST the tags be the common link for related products.
I edited the file /woocommerce/classes/class-wc-products.php
This is pasted starting at line 1192, I commented out a couple of lines.
// Related products are found from category and tag
$tags_array = array(0);
/* $cats_array = array(0); */ /* <-- commented out this line */
// Get tags
$terms = wp_get_post_terms($this->id, 'product_tag');
foreach ($terms as $term) $tags_array[] = $term->term_id;
// Get categories
/* $terms = wp_get_post_terms($this->id, 'product_cat');
foreach ($terms as $term) $cats_array[] = $term->term_id; */ /* <-- and commented out this line */
// Don't bother if none are set
if ( sizeof($cats_array)==1 && sizeof($tags_array)==1 ) return array();
If anyone knows how to make what I’ve done into a line of code to copy to my own theme’s functions.php that would be great since now if I upgrade, I’ll have to manually edit this out again.