Display Current Post’s Position in Custom Taxonomy

If the post order reflect the publishing date (and note that publishing date also takes into account hour, minute and second of publication) than is pretty easy to get the order, using a query that return only post ids and then array_search to find current post id index:

$query = new WP_Query( array(
    'TAXONOMY' => 'TAXONOMY TERM', 
    'posts_per_page' => -1, 
    'post_status' => 'publish',
    'orderby' => 'date', // be sure posts are ordered by date
    'order' => 'ASC', // be sure order is ascending
    'fields' => 'ids' // get only post ids
));

global $post; // current post object

$i = array_search( $post->ID, $query->posts ) + 1; // add 1 because array are 0-based

echo "Post {$i} / {$query->post_count} in TAXONOMY TERM";