Filters get terms in the order the term_ids are listed in the `include` parameter of get_terms.

get-terms-custom-order.php

<?php

add_filter( 'get_terms_args', 'slimline_get_terms_args', 0 ); // allow extra filtering of terms arguments

/**
 * slimline_get_terms_args filter
 *
 * Adds additional filtering to get_terms as needed.
 *
 * @param array $args An array of arguments passed from the get_terms() function
 * @return array $args Arguments after filtering.
 * @since 0.2.0
 */
function slimline_get_terms_args( $args ) {

	if ( 'term__in' === $args[ 'orderby' ] ) {
		add_filter( 'get_terms_orderby', 'slimline_order_terms_by_field', 10, 2 ); // adds SQL FIELD ordering to get_terms
	} // if ( 'term__in' === $args[ 'orderby' ] )

	return $args;
}

/**
 * slimline_custom_order_terms filter
 *
 * Orders terms by the order the ids were entered into the args list
 *
 * @param string $orderby ORDER BY clause of the terms query.
 * @param array $args An array of terms query arguments.
 * @return string $orderby FIELD function if include IDs were set or 'name' if not
 */
function slimline_custom_order_terms( $orderby, $args ) {

	/**
	 * check to see if include IDs have been set
	 *
	 * ORDER BY FIELD() will only work if the "include" parameter is set. If not, change the orderby parameter to "name"
	 * and continue.
	 */
	if ( isset( $args[ 'include' ] ) && ! empty( $args[ 'include' ] ) ) {
	
		// make sure we use a comma-separated list in our SQL statement
		$terms = ( is_array( $args[ 'include' ] ) ? join( ',', $args[ 'include' ] ) : $args[ 'include' ] );

		/**
		 * WordPress joins the wp_terms (t) and wp_term_taxonomy (tt) tables on term_id when using get_terms.
		 * We are using SQL FIELD to order the term_ids based on the order they are entered into the include parameter.
		 */
		$orderby = 'FIELD(tt.term_id,' . $terms . ')';

	} else { // if ( isset( $args[ 'include' ] ) && ! empty( $args[ 'include' ] ) )

		$orderby = 'name';

	} // if ( isset( $args[ 'include' ] ) && ! empty( $args[ 'include' ] ) )

	remove_filter( 'get_terms_orderby', 'slimline_custom_order_terms', 10 ); // don't let this filter alter other queries on the same page

	return $orderby;
}