SELECT 
  p.product_id 
FROM 
  cscart_products as p 
  LEFT JOIN cscart_products_categories as pc ON p.product_id = pc.product_id 
  LEFT JOIN cscart_categories as c ON c.category_id = pc.category_id 
WHERE 
  pc.category_id IN (177, 178, 179, 180, 181, 182) 
  AND p.status = 'A' 
  AND p.parent_product_id = 0 
  AND c.status = 0

Query time 0.00038

JSON explain

{
  "query_block": {
    "select_id": 1,
    "nested_loop": [
      {
        "table": {
          "table_name": "pc",
          "access_type": "range",
          "possible_keys": ["PRIMARY", "pt"],
          "key": "PRIMARY",
          "key_length": "3",
          "used_key_parts": ["category_id"],
          "rows": 25,
          "filtered": 100,
          "attached_condition": "pc.category_id in (177,178,179,180,181,182)",
          "using_index": true
        }
      },
      {
        "table": {
          "table_name": "p",
          "access_type": "eq_ref",
          "possible_keys": ["PRIMARY", "status", "idx_parent_product_id"],
          "key": "PRIMARY",
          "key_length": "3",
          "used_key_parts": ["product_id"],
          "ref": ["cscart_4183_25.pc.product_id"],
          "rows": 1,
          "filtered": 91.16493988,
          "attached_condition": "p.parent_product_id = 0 and p.`status` = 'A'"
        }
      },
      {
        "table": {
          "table_name": "c",
          "access_type": "ref",
          "possible_keys": ["PRIMARY", "p_category_id"],
          "key": "p_category_id",
          "key_length": "3",
          "used_key_parts": ["category_id"],
          "ref": ["cscart_4183_25.pc.category_id"],
          "rows": 1,
          "filtered": 100,
          "attached_condition": "c.`status` = 0",
          "using_index": true
        }
      }
    ]
  }
}