SELECT 
  p.product_id, 
  ifnull(
    count(dp.post_id), 
    0
  ) as discussion_amount_posts 
FROM 
  netting_discussion 
  INNER JOIN netting_products as p ON (
    netting_discussion.object_id = p.product_id
  ) 
  INNER JOIN netting_discussion_posts as dp ON (
    netting_discussion.thread_id = dp.thread_id 
    AND netting_discussion.object_type = 'P'
  ) 
WHERE 
  dp.status = 'A' 
  and p.product_id in (
    531, 570, 592, 569, 707, 757, 761, 834
  ) 
GROUP BY 
  p.product_id

Query time 0.00060

JSON explain

{
  "query_block": {
    "select_id": 1,
    "filesort": {
      "sort_key": "p.product_id",
      "temporary_table": {
        "nested_loop": [
          {
            "table": {
              "table_name": "dp",
              "access_type": "ALL",
              "possible_keys": ["thread_id", "thread_id_2"],
              "rows": 4,
              "filtered": 100,
              "attached_condition": "dp.`status` = 'A'"
            }
          },
          {
            "table": {
              "table_name": "netting_discussion",
              "access_type": "eq_ref",
              "possible_keys": ["PRIMARY", "object_id"],
              "key": "PRIMARY",
              "key_length": "3",
              "used_key_parts": ["thread_id"],
              "ref": ["pucuda_cscart.dp.thread_id"],
              "rows": 1,
              "filtered": 100,
              "attached_condition": "netting_discussion.object_type = 'P'"
            }
          },
          {
            "table": {
              "table_name": "p",
              "access_type": "eq_ref",
              "possible_keys": ["PRIMARY"],
              "key": "PRIMARY",
              "key_length": "3",
              "used_key_parts": ["product_id"],
              "ref": ["pucuda_cscart.netting_discussion.object_id"],
              "rows": 1,
              "filtered": 100,
              "attached_condition": "p.product_id in (531,570,592,569,707,757,761,834)",
              "using_index": true
            }
          }
        ]
      }
    }
  }
}