The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
2. Replace In Subquery With Correlated Exists (modified query below): In many cases, an EXISTS subquery with a correlated condition will perform better than a non correlated IN subquery.

Optimal indexes for this query:

CREATE INDEX table_x_idx_day ON "table_x" ("day");
CREATE INDEX table_y_idx_prop_id ON "table_y" ("prop","id");

The optimized query:

SELECT
        date_trunc('month',
        table_x.day) AS month,
        sum(table_x.total) 
    FROM
        table_x 
    WHERE
        EXISTS (
            SELECT
                1 
            FROM
                table_y 
            WHERE
                (
                    table_y.prop = 'xyz'
                ) 
                AND (
                    table_x.y_id = table_y.id
                )
        ) 
        AND table_x.day BETWEEN '2015-11-05' AND '2016-11-04' 
    GROUP BY
        month