MySQL 8.0

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WITH yourTable AS (
    SELECT 1 AS id, '2017-01-01' AS start_date, '2017-07-01' AS end_date UNION ALL
    SELECT 2,  '2017-01-15', '2017-07-12' UNION ALL
    SELECT 3,  '2017-02-01', '2017-08-01' UNION ALL
    SELECT 4,  '2017-03-01', '2017-08-01' UNION ALL
    SELECT 5,  '2017-03-12', '2017-08-12' UNION ALL
    SELECT 6,  '2017-03-30', '2017-08-30' UNION ALL
    SELECT 7,  '2017-05-01', '2017-11-01' UNION ALL
    SELECT 8,  '2017-06-01', '2017-12-01' UNION ALL
    SELECT 9,  '2017-07-01', '2018-01-01' UNION ALL
    SELECT 10, '2017-08-01', '2018-02-01' UNION ALL
    SELECT 11, '2018-01-01', '2018-07-01' UNION ALL
    SELECT 12, '2018-02-01', '2018-08-01' UNION ALL
    SELECT 13, '2018-03-01', '2018-09-01'
)

SELECT
    c.month,
    COUNT(t.start_date) AS num_subscriptions
FROM
(
    SELECT '2017-01-01' AS month UNION ALL
    SELECT '2017-02-01' UNION ALL
    SELECT '2017-03-01' UNION ALL
    SELECT '2017-04-01' UNION ALL
    SELECT '2017-05-01' UNION ALL
    SELECT '2017-06-01' UNION ALL
    SELECT '2017-07-01' UNION ALL
    SELECT '2017-08-01' UNION ALL
    SELECT '2017-09-01' UNION ALL
    SELECT '2017-10-01' UNION ALL
    SELECT '2017-11-01' UNION ALL
    SELECT '2017-12-01' UNION ALL
    SELECT '2019-01-01' UNION ALL
    SELECT '2018-02-01' UNION ALL
    SELECT '2018-03-01' UNION ALL
    SELECT '2018-04-01' UNION ALL
    SELECT '2018-05-01' UNION ALL
    SELECT '2018-06-01' UNION ALL
    SELECT '2018-07-01' UNION ALL
    SELECT '2018-08-01' UNION ALL
    SELECT '2018-09-01' UNION ALL
    SELECT '2018-10-01' UNION ALL
    SELECT '2018-11-01' UNION ALL
    SELECT '2018-12-01'
) c
LEFT JOIN yourTable t
    ON c.month <= t.end_date AND LAST_DAY(c.month) >= t.start_date
GROUP BY
    c.month;

month	num_subscriptions
2017-01-01	2
2017-02-01	3
2017-03-01	6
2017-04-01	6
2017-05-01	7
2017-06-01	8
2017-07-01	9
2017-08-01	8
2017-09-01	4
2017-10-01	4
2017-11-01	4
2017-12-01	3
2019-01-01	0
2018-02-01	3
2018-03-01	3
2018-04-01	3
2018-05-01	3
2018-06-01	3
2018-07-01	3
2018-08-01	2
2018-09-01	1
2018-10-01	0
2018-11-01	0
2018-12-01	0