SELECT 
  p.product_id, 
  ifnull(
    count(dp.post_id), 
    0
  ) as discussion_amount_posts 
FROM 
  jmj_discussion 
  INNER JOIN jmj_products as p ON (
    jmj_discussion.object_id = p.product_id
  ) 
  INNER JOIN jmj_discussion_posts as dp ON (
    jmj_discussion.thread_id = dp.thread_id 
    AND jmj_discussion.object_type = 'P'
  ) 
WHERE 
  dp.status = 'A' 
  and p.product_id in (
    1676, 811, 812, 891, 892, 893, 929, 930, 
    982, 950, 955, 957, 959, 961, 964, 966, 
    834, 835, 836, 837, 838, 839, 840, 841, 
    842, 843, 845, 846, 847, 849, 850, 851, 
    852, 853, 854, 855, 859, 860, 861, 910, 
    916, 1531, 1534, 1439
  ) 
GROUP BY 
  p.product_id

Query time 0.01118

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "10.65"
    },
    "grouping_operation": {
      "using_temporary_table": true,
      "using_filesort": true,
      "cost_info": {
        "sort_cost": "0.17"
      },
      "nested_loop": [
        {
          "table": {
            "table_name": "dp",
            "access_type": "ALL",
            "possible_keys": [
              "thread_id",
              "thread_id_2"
            ],
            "rows_examined_per_scan": 25,
            "rows_produced_per_join": 2,
            "filtered": "10.00",
            "cost_info": {
              "read_cost": "6.78",
              "eval_cost": "0.50",
              "prefix_cost": "7.28",
              "data_read_per_join": "1K"
            },
            "used_columns": [
              "post_id",
              "thread_id",
              "status"
            ],
            "attached_condition": "(`jmj_test`.`dp`.`status` = 'A')"
          }
        },
        {
          "table": {
            "table_name": "jmj_discussion",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY",
              "object_id"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "thread_id"
            ],
            "key_length": "3",
            "ref": [
              "jmj_test.dp.thread_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "6.71",
            "cost_info": {
              "read_cost": "2.50",
              "eval_cost": "0.03",
              "prefix_cost": "10.28",
              "data_read_per_join": "4"
            },
            "used_columns": [
              "thread_id",
              "object_id",
              "object_type"
            ],
            "attached_condition": "((`jmj_test`.`jmj_discussion`.`object_id` in (1676,811,812,891,892,893,929,930,982,950,955,957,959,961,964,966,834,835,836,837,838,839,840,841,842,843,845,846,847,849,850,851,852,853,854,855,859,860,861,910,916,1531,1534,1439)) and (`jmj_test`.`jmj_discussion`.`object_type` = 'P'))"
          }
        },
        {
          "table": {
            "table_name": "p",
            "access_type": "eq_ref",
            "possible_keys": [
              "PRIMARY"
            ],
            "key": "PRIMARY",
            "used_key_parts": [
              "product_id"
            ],
            "key_length": "3",
            "ref": [
              "jmj_test.jmj_discussion.object_id"
            ],
            "rows_examined_per_scan": 1,
            "rows_produced_per_join": 0,
            "filtered": "100.00",
            "using_index": true,
            "cost_info": {
              "read_cost": "0.17",
              "eval_cost": "0.03",
              "prefix_cost": "10.48",
              "data_read_per_join": "812"
            },
            "used_columns": [
              "product_id"
            ]
          }
        }
      ]
    }
  }
}