Should a meta_key or other key-value table columns use a HASH or BTREE index? I've noticed that my WordPress database has BTREE indexes everywhere.
By my understanding, BTREE indexes allow more efficient &lt; &gt; and BETWEEN queries, but are otherwise less efficient than a HASH query for = and != queries.
This makes sense for some columns that might be filtered numerically (dates obviously, and IDs potentially, – though in practice ID &gt; x doesn't seem very likely in WordPress), but I can't see any benefit for columns like meta_key which stores the text key of a key-value pair, or indeed the post_id column of a post_metadata table, which will almost without exception be JOINed to the posts table.
Would a HASH index be more performant? If so, is there any reason that my database is using BTREE indexes for these columns, or is this just a default? If not, what am I lacking in my understanding of indexes?
That's the wrong question.  The indexes that WP provides on the meta tables are inefficient.  (And the general EAV pattern sucks.)
This explains how to significantly improve the indexes:  http://mysql.rjweb.org/doc.php/index_cookbook_mysql#speeding_up_wp_postmeta
Back to your question:  BTree is about as fast as Hash (were it to exist).  And Hash is not available for InnoDB.  (InnoDB is the only 'engine' you should use for WP.)
I believe that the developer of InnoDB saw that &quot;one side does fit all&quot; when he implemented only BTree.