Filter wp_dropdown_categories by post type.

## basic-dropdown-usage.php
<?php
/**
 * Using wp_dropdown_categories with the post type filter applied.
 *
 * @link https://joshuadnelson.com/category-taxonomy-dropdown-filtered-by-post-type/
 */

// Taxonomy dropdown arguments
$args = array(
	'taxonomy'		=> 'department',
	'post_type'		=> 'project', // filter by the post type 'project'
	'echo'			=> true,
);
wp_dropdown_categories( $args );

## filter-term-clauses.php
<?php
/**
 * Filter the term clauses using the arguments, specifically for the wp_dropdown_categories.
 *
 * @see http://wordpress.stackexchange.com/questions/207655/restrict-taxonomy-dropdown-to-post-type
 * @see https://www.dfactory.eu/get_terms-post-type/
 *
 * @param array $clauses
 * @param string $taxonomy
 * @param array $args
 *
 * @return array
 */
add_filter( 'terms_clauses', 'jdn_post_type_terms_clauses', 10, 3 );
function jdn_post_type_terms_clauses( $clauses, $taxonomy, $args ) {
	// Make sure we have a post_type argument to run with.
	if( !isset( $args['post_type'] ) || empty( $args['post_type'] ) )
		return $clauses;

	global $wpdb;

	// Setup the post types in an array
	$post_types = array();

	// If the argument is an array, check each one and cycle through the post types
	if( is_array( $args['post_type'] ) ) {

		// All possible, public post types
		$possible_post_types = get_post_types( array( 'public' => true ) );

		// Cycle through the post types, add them to our array if they are public
		foreach( $args['post_type'] as $post_type ) {
			if( in_array( $post_type, $possible_post_types ) )
				$post_types[] = "'" . esc_attr( $post_type ) . "\'";
		}

	// If the post type argument is a string, not an array
	} elseif( is_string( $args['post_type'] ) ) {
		$post_types[] = "'" . esc_attr( $args['post_type'] ) . "'";
	}

	// If we have valid post types, build the new sql
	if( !empty( $post_types ) ) {
		$post_types_string = implode( ',', $post_types );
		$fields = str_replace( 'tt.*', 'tt.term_taxonomy_id, tt.term_id, tt.taxonomy, tt.description, tt.parent', $clauses['fields'] );

		$clauses['fields'] = 'DISTINCT ' . esc_sql( $fields ) . ', COUNT(t.term_id) AS count';
		$clauses['join'] .= ' INNER JOIN ' . $wpdb->term_relationships . ' AS r ON r.term_taxonomy_id = tt.term_taxonomy_id INNER JOIN ' . $wpdb->posts . ' AS p ON p.ID = r.object_id';
		$clauses['where'] .= ' AND p.post_type IN (' . $post_types_string . ')';
		$clauses['orderby'] = 'GROUP BY t.term_id ' . $clauses['orderby'];
	}

    return $clauses;
}

## get-custom-taxonomy-dropdown.php
<?php
/**
 * A wrapper function for the custom dropdown, sets the current value by a url query var,
 * adds a custom label, and a wrapper element.
 *
 * @author Joshua David Nelson, josh@joshuadnelson.com
 *
 * @link https://joshuadnelson.com/category-taxonomy-dropdown-filtered-by-post-type/
 *
 * @see https://codex.wordpress.org/Function_Reference/wp_dropdown_categories
 *
 * @param array $args
 *
 * @return string $output
 */
function jdn_get_custom_taxonomy_dropdown( $args ) {

	// Taxonomy dropdown arguments
	$defaults = array(
		'taxonomy'		=> false, 	// required, the default here is a failsafe
		'post_type'		=> false, 	// pass a value if you want to
		'echo'			=> false, 	// true to echo, false for return
		'label'			=> false, 	// false or pass a string for the label
		'query_var'		=> false, 	// pass the query variable for the selected dropdown value
		'id'			=> '', 		// set this and the default category 'name' argument
		'wrap'			=> 'div', 	// the wrapper element. set to false to skip it.
		'wrap_class'		=> 'select-wrap', // The custom wrapper class, set to false to skip it
	);
	$args = wp_parse_args( $args, $defaults );

	// Be sure we're good to go.
	if( ! $args['taxonomy'] )
		return false;

	// Current value of query variable, if there is one
	if( $args['query_var'] ) {
		$query_tax = get_query_var( esc_attr( $args['query_var'] ), false );
		$current = $query_tax ? sanitize_text_field( $query_tax ) : '';
		$args['selected'] = $current;
	}

	// We're returning the output of wp_dropdown_cateogies, but we need to know how the end user wants it back in this function,
	// so we'll store that value as a variable and reset the echo argument for the wp_dropdown_categories.
	$echo = esc_attr( $args['echo'] );
	$args['echo'] = false;

	// Grab the category dropdown
	$tax_drop = wp_dropdown_categories( $args );

	// Add a label
	$label = ( $args['label'] && !empty( $args['id'] ) ) ? '<label for="' . esc_attr( $args['id'] ) . '">' . esc_attr( $args['label'] ) . '</label>' : '';

	// Wrap it up
	$class = $args['wrap_class'] ? ' class="' . esc_attr( $args['wrap_class'] ) . '"' : '';
	$tax_drop = ( $args['wrap'] && !empty( $tax_drop ) ) ? '<' . esc_attr( $args['wrap'] ) . $class . '>' . $label . $tax_drop . '</' . esc_attr( $args['wrap'] ) . '>' : $tax_drop;

	// Return it or echo it back
	if( $echo ) {
		echo $tax_drop;
	} else {
		return $tax_drop;
	}
}